Before just hauling to events, I would haul to outside stables, open arenas, ect to first get her used to being in new places before throwing all the commotion that goes on during a show at her. Also, make sure she can consistently and reliably LOAD :) Nothing worse than being stuck somewhere with a horse that says NO to the trailer.
As far as training, make sure your horse can back, side pass, steer off your legs, pivot, turn on the forehand, and stop with little to no rein aid as well as give to the bit laterally in both directions.
When it gets to show time, pack the trailer the night before, and make a checklist if you have to so you don't forget anything. Also, be sure to get there early so you have time to warm up and get her comfortable in the arena she'll be running in. Take this time to check for rough, deep, or rocky parts in the arena sand. Before your run, keep yourself calm! If you are overly nervous or excited, that horse is gonna feel it and be a little more gassy, flighty, ignore your aids, ect. Also, be sure to check attire rules for your association so you don't get disqualified for not having a hat or something.
Oh, and HAVE FUN!!