If you're safe, you're ready! As long as you can control your horse, and aren't a danger to others, it's never to early to try entering in a horse show. (in appropriate classes, of course) Horse shows can be a fun and rewarding experience that help develop your bond with your horse.
You'll learn a LOT your first few shows. Don't expect to place, or place well, but focus on the experience. If you don't fall off you're doing better than half the first timers out there! Instead of focusing on winning, just focus on enjoying your horse and doing your best. Use your first show season to study winning horses and riders. Try to watch other classes and see what a winning ride looks like, and if at all possible try to speak with the judge after the show, THANK them, and politely ask a question like "What do I most need to improve?" "Do you have any suggestions of how I can improve my performance next time?" Most judges are very happy to answer those questions if they have time.
A walk/trot class is the best first class for most new riders. Remember you always have the option to choose not to ride the gait the announcer calls. You'll immediately be marked down to last place if you choose not to trot in a walk trot or not to canter in your first few canter classes, but staying in control of your horse and having a positive experience is better than putting yourself or someone else in danger!
To prepare for your first horse show you should be sure your horse is comfortable in an arena with other horses. If possible, the week before your show trailer to the arena where the show will be held and practice with a few friends.