Almost all the Time Lord regenerations I've seen on-screen have been of adult Time Lords, who typically have already lived for several hundred years. Do we know whether or not a very young Gallifreyan could regenerate, either deliberately, by force, or naturally after some mortal wound? Or do they have to reach a certain age first?
Children can regenerate. For example, a very young
River Song/Melody Pond
regenerates at the end of "Day of the Moon." The exact age of the character is not given, but she was played by Sydney Wade, who Google informs me was born in 2001, and the episode aired in 2011.
That being said, this character's ability to regenerate in general is said (in "A Good Man Goes to War") to be the result of having been conceived in the Time Vortex, so she should probably not be taken as typical.
The same conversation includes the claim that Time Lords, in contrast, "became what they did [including having regeneration ability] through prolonged exposure to the Time Vortex. The Untempered Schism..." over the course of billions of years. Given this, and given the fact that gazing into the Untempered Schism is so important a part of Time Lord training that everyone who goes to the Academy has to do it even though it drives many of them insane, one might guess that Time Lords wouldn't be able to regenerate until then. But this is pure speculation.
The thing is that there are no baby TimeLords (with exceptions). There are born Gallifreyans, and then, they are made Timelords in the Academy.
In the end of Listen you hear the Doctor's parents saying that he will never be a TimeLord.
I believe that only the TimeLords are able to regenerate, not the Rest of Gallifreyans. For what I have see, there is no point that it is said that Gallifreyans doesn't regenerate, but it has been talked as a exclusive quality of the TimeLords.
Based on what little we know, it's most likely that Gallifreyans possess the potential to regenerate from birth, but can't actually do so until that ability is acquired as part of Time Lord training.
It's actually not all that clear (of course not, it's Doctor Who) how the regeneration process works. We know some of the outward behaviors, but very little about the inner mechanics. But most of the evidence points to regeneration probably being a latent genetic ability that has to be "activated" by the Time Lords.
The Untempered Schism
The most direct explanation how Time Lords regeneration ability came to be comes from Vastra in "A Good Man Goes To War":
VASTRA: You've told me about your people. They became what they did through prolonged exposure to the time vortex. The Untempered Schism.
DOCTOR: Over billions of years. It didn't just happen.
VASTRA: So how close is she? Could she even regenerate?
The untempered schism is a kind of "hole" in the universe where unfiltered Time Vortex energy is seeping into the universe. We also know, from "The End of Time", that Time Lord cadets are exposed to the untempered schism at a very young age. So, it's clear that this untempered schism is a big part of Time Lord development.
Vastra says that The Doctor's "people" "became what they did" because of the Schism, and The Doctor claims that it was a very long process. If we assume that she's at least partly talking about his regeneration ability, if it developed over billions of years, it would need to be genetic. That means that Time Lord genetics almost certainly does include the ability to regenerate, from birth.
Time Lords Are Gallifreyans
However, we're also pretty sure that Time Lords are genetically Gallifreyan. In the revived series, we've learned a lot more about The Doctor's youth, and it's pretty obvious that he wasn't guaranteed to become a Time Lord. He was taken from his parent at a young age to be trained, and had to be accepted. In "Listen", for example, The Doctor's parents worry that he might never become a Time Lord due to his fear.
It seems unlikely that all Gallifreyans can regenerate a half-dozen times each. There's an entire population of "peasant" Gallifreyans who aren't Time Lords. We have never seen anything to indicate that these people can also regenerate. I would expect such an ability to fundamentally change they way those people worked, lived, dealt with war, etc.
Time Lord Control
It's also interesting to note how much control the High Council has over a Time Lord's regeneration. They've granted both The Doctor (on Trenzaloee) and The Master (during the Time War) a new set. They've also claimed they can take them away, and we've seen them force regeneration on The Doctor as well. What this tells us is that the 12-regeneration limit probably isn't genetically hard-coded. It seems to be something imposed by the High Council on Time Lords as they are inducted.
By itself, this isn't very definitive; they may just have a lot of control over a normal biological process. But the casual way in which the High Council, especially Rassilon, seems to treat regeneration as almost a bargaining chip implies that it's not an inherent, natural right of a Time Lord to do it.
What About Melody?
Melody Pond is an interesting case. She seems to validate the idea that Time Lords can regeneration as soon as they're born. A young Melody Pond, having never been anywhere near Gallifrey or a Time Lord, regenerates after escaping from the spacesuit. She regenerates at least one more time after being shot in "Let's Kill Hitler".
But it's important to remember three things:
- She's not really Gallifreyan
- Her birth is an anomaly.
- The Silence were clearly "doing research" on her in utero.
Melody was conceived and spent at least part of her early gestation period in the Time Vortex. This is almost certainly not normal for Gallifreyans to do, so we can't really extrapolate her case to the general case. In addition, we know that the Silence were looking for someone like her to fight The Doctor, so it's entirely possible that they did something to activate her ability to regenerate at a young age.