It is indeed a change-of-state 了, more specifically, an "already" 了.
If this 了 is a change-of-state 了, then (to my understanding) this question can only be asked on the kid's birthday.
This isn't necessarily true, although on a kid's birthday you surely will ask the kid 你几岁了？instead of 你几岁呀？. The 了, in this particular scenario, does mean that the kid turns this age (the change of state) on this particular day.
But in other situations, 你几岁了？can still make sense. 刘月华(Liu Yuehua) et al.'s 《实用现代汉语语法》(Practical Modern Chinese Grammar) states that the 了 particle can be used to emphasise "时间、季节、年龄、数量的更迭变化" (the successive change of time, seasons, age or number). Therefore, there's a slight semantic difference between 你几岁了/你多大了/你多大年纪了？(with 了) and 你几岁呀？(without 了). It will be clearer if we observe the declarative form:
我三岁，她五岁。I'm three, and she's five. (stating a fact)
我三岁了。 I've already turned three (this year). / I'm three (isn't it cool?!). (emphasising the passage of time)
(A middle-aged person:)
我今年五十五。 I'm fifty-five this year. (stating a fact)
我今年五十五了。I've turned fifty-five this year. (emphasising the passage of time)
我都五十五了，你还让我干这个？I'm already fifty-five, and you're making me do this? (if there's a 都 or 已经 in this sentence, omitting 了 won't sound natural to a Mandarin speaker's ears)
今年我九十八，明年就九十九了。 This year I'm ninety-eight, so the next year I'll turn ninety-nine. (in the first clause, this person's age, ninety-eight, is just a passing mention, a statement of fact; but in the second clause, they want to emphasise the fact that time flies and they'll be ninety-nine)
So, if you consider the following imaginary conversation:
(The reporter:) 您今年多大年纪了？ How old are you this year?
(The interviewee:) 一百一十七了。 Already 117 years old.
The reporter is asking How old are you already?, because 117 is a stunning age. This is emphasising the passage of time. Now, if it's not an reporter but a tired census taker who just cares about the facts, the question has a good chance to be presented as a mere 您今年多大年纪？
Or, consider a friend coming to a couple's house and cooing to their little kid, 你几岁了呀？ It will usually come with a tone of look at this little thing aww look how big you have become how many years have you been in this cruel world little darling or whatever people who like kids will think upon meeting a kid - it's about the change and passing of time, or to put it simply, a sense of already.