Really Syl, it's up to you!
In my opinion, it depends on how young your character is. For example, if they're not quite yet Hogwarts age (or even a first or second year), I wouldn't apply just yet. Obviously pre-Hogwarts would be way too young to have the ability and a first or second year wouldn't have anywhere close to the required levels for transformation.
However, if the character is older and advancing through school (attending classes and earning levels), you might want to consider applying for the special request then. Of course, the student wouldn't be able to be an animagus right out (the levels requirements are at least C15 and T15), but you could apply for them to start to learn and acquire the ability (focus classes on transfig/charms, study with a professor, RP borrowing books from the library on the subject, etc.).
Does this answer your question?
