I don't think there are laws against young witches and wizards flying before the age of eleven and before they get to Hogwarts. From Philosopher's Stone:
‘You don’t know you’ll make a fool of yourself,’ said Ron reasonably. ‘Anyway, I know Malfoy’s always going on about how good he is at Quidditch, but I bet that’s all talk.’
Malfoy certainly did talk about flying a lot. He complained loudly about first-years never getting in the house Quidditch teams and told long, boastful stories which always seemed to end with him narrowly escaping Muggles in helicopters. He wasn’t the only one, though: the way Seamus Finnigan told it, he’d spent most of his childhood zooming around the countryside on his broomstick. Even Ron would tell anyone who’d listen about the time he’d almost hit a hang-glider on Charlie’s old broom. Everyone from wizarding families talked about Quidditch constantly. [...] Neville had never been on a broomstick in his life, because his grandmother had never let him near one.
Philosopher's Stone - page 107 - Bloomsbury - chapter 9, The Midnight Duel
And then an excerpt from a letter from Lily Potter to Sirius Black:
Thank you, thank you, for Harry’s birthday present! It was his favourite by far. One year old and already zooming along on a toy broomstick, he looked so pleased with himself, I’m
enclosing a picture so you can see. You know it only rises about two feet off the ground, but he nearly killed the cat and he smashed a horrible vase Petunia sent me for Christmas (no complaints there). Of course, James thought it was so funny, says he’s going to be a great Quidditch player, but we’ve had to pack away all the ornaments and make sure we don’t take our eyes off him when he gets going. [...]
Deathly Hallows - page 149 - Bloomsbury - chapter 10, Kreacher's Tale
At last, lying face down on the floor he spotted what looked like a torn piece of paper under the chest of drawers. When he pulled it out, it proved to be most of the photograph Lily had described in her letter. A black-haired baby was zooming in and out of the picture on a tiny broom, roaring with laughter, and a pair of legs that must have belonged to James were chasing after him.
Deathly Hallows - page 151 - Bloomsbury - chapter 10, Kreacher's Tale
Sorry, that was a lot of quotes there. But I wanted to show that it appears the use of a broom is discretionary and up to the parent(s) to decide when a child is ready to ride a broom. Lily's letter would have been written after Harry's first birthday (as she and James didn't survive to see his second or him grow up) and the little toy broom he was riding actually levitated off the ground. On the other hand, there's Neville, whose grandmother forbade him to try riding a broom even though, as it appears, all the other children his age were learning how to fly. I think perhaps brooms don't violate the Statute for Underage Use of Magic because they are already charmed by the time they are ready to be sold. In Chamber of Secrets, Fred and George explain that they are not violating the Statute for Underage Magic by flying the Ford Anglia because the car belongs to Mr Weasley and he's the one who put all the charms on it, and they are just borrowing it.
Brooms are the official legal means of transportation in British wizarding families, according to Quidditch Through the Ages:
We are so accustomed these days to the fact that every wizarding household in Britain owns at least one flying broomstick that we rarely stop to ask ourselves why. Why should the humble broom have become the one object legally allowed as a means of wizarding transport?
Quidditch Through the Ages - page 1 - Scholastic - chapter 1, The Evolution of the Flying Broomstick
As every school-age wizard knows, the fact that we fly on broomsticks is probably our worst-kept secret.
Quidditch Through the Ages - page 16 - Scholastic - chapter 5, Anti-Muggle Precautions
It makes sense that witches and wizards would begin learning to fly on broomsticks as early as possible (Or, in Neville's case, as soon as he was out of the clutches of his grandmother!). As the only legal means of transportation, should there be an emergency, the younger witches and wizards should know how to fly for safety reasons. You probably remember from Half-Blood Prince that Apparition is not legally allowed until age seventeen. Transportation such as the Ford Anglia is probably highly unusual in private families. So the broom has to be it.