I've had several horses (well 3) and it depends entirely on how quickly you and the horse get to know each other. It takes longer with some and with others you just bond almost straight away.
i got Gem when i was 12 (so may not be the best to ask as i was SO keen to get her out!)
I think it was about 2 weeks from owning her before i entered a XC competition! (I WAS mad!!)
Just make sure your first one isnt too far away, a friendly local village show or something. and only enter one or two classes where you can just get used to the atmosphere.
I think it depends entirely on the individual & how comfortable you feel on the horse/ what the horse is like and what level you are competing at etc.
I have tried horses out at shows and have taken one to a show two days after it arrived, but that was a while ago when I was competing quite a bit.
I would say that if you are comfortable & confident and your horse is not a baby & it is a local show then why not go for it?