Congratulations on your decision to run! Rodeo queening is a ton of fun, but do expect to put in some elbow grease.
I just gave someone advice on rodeo queening not too long ago. That thread is here Rodeo Queening
I will let you read through that. Please feel free to ask me any other additional questions you have. I would love to help!
I do agree that it is an excellent idea to ask the girls who have won in past years as they have been to the pageant and know what to expect. I would also advise you to go watch any other pageants that are happening before yours. You can learn a lot even from just being a spectator. And it is a very good idea to have a pageant coach. Even the current Miss Rodeo America has a pageant coach.
I took a peek at your pageant website and this is the first pageant I have seen where they are including points for things other than appearance, horsemanship, and personality. But any rodeo queen pageant can do as they please! You'll see that horsemanship and public relations carry the most weight.
For horsemanship, it's the little details that make a difference. Smile ALL the time. Look like you are enjoying it! Keep your body relaxed. Do not allow your reins to touch the ground if you dismount in front of the judge, and you'll be using split reins, not barrel reins. It sounds like you will need to dismount at the judges so that they can ask you horse anatomy question (so be sure to study!!!) Stay at your horse's shoulder when you mount and just turn the stirrup toward you; do not try to mount by the horse's ribcage or further back. Keep your leg straight and poised as your swing it over. And I can just keep spurting about those little details like that. It makes you look polished.
As far as public relations, get yourself practice doing interviews and speaking! Ask your rodeo friends to quiz you on rodeo knowledge and personality questions. Get a small audience together to practice your speeches, and make sure to practice in front of a mirror by yourself too. Video yourself doing your speech and watch it. Be yourself!!! Don't use generic fake answers you think the judges want to hear. They want to see YOU and your personality. Show it!
But you only have two months to prepare so get cracking!!!! You've got to get outfits together, practice modeling (which you will be doing), write and memorize your speeches, create and practice horsemanship patterns, and study, study, study, and study some more!