No. If anything, magical children have a safer upbringing than Muggles.
Perhaps it's stating the obvious but JK Rowling hasn't provided any firm statistics on childhood mortality and injuries in the books or supplementary materials (why would she?). But I think it's possible to answer this question by looking at the childhood deaths that occur in the books and working outwards to guesstimate how common these sorts of incidents were - and how they relate to Muggle statistics.
There are three children who die in the books:
- Colin Creevey
- Cedric Diggory
- Ariana Dumbledore
I'm counting children by the wizarding world's own definition of 'under 17s'. Vincent Crabbe and possibly Lavender Brown also died but they were in Harry's year and so were presumably 'of age'.
Of these three deaths, Dumbledore's was accidental, Diggory's was murder and Creevey's was as a result of war. Diggory's death was done using Dark Arts and triggered the start of the Second Wizarding War so I'm doing to treat his and Creevey's death as belonging to a separate category.
Ariana Dumbledore died because she was caught in the crossfire of a magical duel. This situation wasn't typical for magical children but might conceivably be thought to be part of the dangers of living in a magical household. Yet Ariana is the only magical child that we hear of who dies in peacetime. This would seem to be a very low childhood mortality rate.
Let's put some numbers on it. It's been estimated that there are roughly 10,000 witches and wizards living in Britain during the era that the books are set. Let's say then, to make the numbers easier, that there are very roughly 1,000 under-17s living in magical households at any given moment. Ariana's death gives us a childhood death rate of 1 in every 1,000. That compares with an infant mortality rate of 3.7 deaths per 1,000 live births for Muggles in England and Wales under one. The mortality rate for ages 1-15 is 10 in every 100,000, or 0.1 per 1,000. So whilst deaths between the ages of 1 and 16 in Muggles are quite uncommon, the figures for under 1s alone gives us a higher death rate than the wizarding world. Even if there are other magical deaths that we're not hearing about, the mortality rate is still lower overall than it is for Muggles.
Creevey and Diggory's deaths obviously create a spike in the numbers. It's conceivable that so many kids died in the Battle of Hogwarts that, for that year alone, there were more wizarding deaths than Muggle deaths. Yet comparing a warzone with peacetime England and Wales isn't really a fair contrast. Imagine how many children are currently dying in somewhere like Syria. UNICEF estimates that there were at least 652 childhood deaths in 2016, although sadly this is likely a very conservative figure. It's difficult to imagine that there would be a higher childhood mortality rate in a wizarding war than there would in a Muggle one. In Muggle wars many of the deaths come about as a result of water shortages, a lack of medical facilities and citizens getting caught up in mortar fire. These aren't the sorts of issues which crop up in a magical war, where the fighting largely happens in short bursts and in hand-to-hand combat. Whilst we have no firm data to prove it, I think it's unlikely that 2 deaths per 1,000 would exceed the number of Muggle deaths in times of war.
Why do comparatively few children die in the Harry Potter universe, despite the range of magical and non-magical dangers? Basically, because they are more resilient than Muggles.
I decided that, broadly speaking, wizards would have the power to correct or override 'mundane' nature, but not 'magical' nature. Therefore, a wizard could catch anything a Muggle might catch, but he could cure all of it; he would also comfortably survive a scorpion sting that might kill a Muggle, whereas he might die if bitten by a Venomous Tentacula. Similarly, bones broken in non-magical accidents such as falls or fist fights can be mended by magic, but the consequences of curses or backfiring magic could be serious, permanent or life-threatening...Thus it can be seen that while wizards have an enviable head start over the rest of us in dealing with the flu, and all manner of serious injuries, they have to deal with problems that the rest of us never face.
(Pottermore, "Illness and Disability).
So magical kids are vulnerable to magical threats, but pretty much immune to the sort of things that might harm a Muggle. And even a lot of magical diseases and injuries can be healed with time.
To deal with the specific points in the question:
Unconscious magic. As Adamant says, this kind of magic isn't a serious danger to the children. If anything it acts to protect magical children from serious harm. Hence Neville cushions himself when he falls out the window and Harry leaps onto the school roof when running away from Dudley and his gang.
Under 11s aren't allowed wands and so aren't able to do actual spells. They wouldn't need as much supervision as the question implies. Their unconscious magic is tied to emotion and is mostly harmless.
Quidditch Quidditch is a dangerous sport, no doubt about it. But there have never been any fatalities at Hogwarts.
"Er - have the Bludgers ever killed anyone?" Harry asked, hoping he sounded offhand.
"Never at Hogwarts. We've had a couple of broken jaws but nothing worse than that."
(Philosopher's Stone, Chapter 10, Halloween)
As Rowling explains in the Pottermore article above, most of the serious physical injuries that one can pick up playing Quidditch can be healed fairly easily by magic. Even faulty magic can be repaired eventually.
"You should have been brought straight to me!" she raged, holding up the sad, limp remainder of what, half an hour before, had been a working arm. "I can mend bones in a second - But growing them back- "
"You will be able to, won't you?" said Harry desperately.
"I'll be able to, certainly, but it will be painful," said Madame Pomfrey grimly...
(Chamber of Secrets, Chapter 10, The Rogue Bludger).
Schoolyard dueling Yes, there is the potential for students to injure one another if they get into fights. There isn't much chance to get involved in these, though. Magic is forbidden in the corridors between lessons and the teachers are more than capable of protecting the kids from doing any real harm during classes. Besides, even when fights do break out, most of the kids are too inept to do any real damage to one another.
"Well, a second's there to take over if you die," said Ron casually, getting started at last on his cold pie. Catching the look on Harry's face, he added quickly, "but people only die in proper duels, you know, with real wizards. The most you and Malfoy'll be able to do is send sparks at each other. Neither of you knows enough magic to do any real damage."
(Philosopher's Stone, Chapter 9, The Midnight Duel).
The Killing Curse is certainly beyond them.
"Avada Kedavra's a curse that needs a powerful bit of magic behind it - you could get your wands out now and point them at me and say the words, and I doubt I'd get so much as a nose-bleed."
(Goblet of Fire, Chapter 14, The Unforgivable Curses).
The only really serious incident that came about as a result of kids attacking one another was Malfoy being hit by Sectumsempra. This was a potentially fatal injury but even when this dangerous Dark spell is used Snape is able to patch Malfoy up and get him back to full health.
In conclusion, witches and wizards aren't shown to die at any higher rate than Muggles. If anything, their mortality rates are probably lower. Magical kids face considerable risks but many of these risks can also be counteracted by magic, which actually makes growing up as a witch or wizard a pretty safe experience.