Why? It's easier and takes less time & effort the earlier you do it (and you're massively more likely to be able to get a great party - they do tend to get booked up ahead of time!)
How far in advance should I book?
The short answer is... as far as you can! The most popular children’s parties tend to get booked up a couple of months in advance.
I'd say you want to get your invitations out 5 weeks before the party - so you want to work backwards from that point!