Hermione was born September 19th, so we actually know the deadline. But I fully accept your version that Snape took his son in early.
Author's Response: Hogwarts is different than Muggle schools in any case... most muggle public schools (in real life) have Sept 1 as the deadline (at least in America), but at the age of 11 one or two months really doesn't make a difference like they say it does at earlier ages like 5 or 6, so I'm going to say that in my magic world, Hogwarts accepts anyone with a birthday by December. Anyway, does it actually say anywhere that Hermione just made the deadline, or only that her birthday is September 19?
Thanks for commenting!