Me? I didn't enter a judo tourney, but I did enter a grappling tourney after 4 months. Lost miserably, but heck, it was worth it.
It depends actually. Some people are just born talented and can enter after 2-3 month and do quite well. Some people are so dense and daft, even when they're a black belt, they still don't want/shouldn't enter a tourney.
Aikiuke, I'd say, seeing as you have been in Aikido for a couple of years (5 years?) you could enter at around 4 months or so and have very little problem.
Just remember, don't go around doing wristlocks on them judo-ka even though it's effective when they grab you (it's a sport, not self-defense
Need any tips and tricks, feel free to ask.