Age isn't a barrier. Get your mom to help or find another adult who will. It's not that hard and the delegate will walk you through most of the process. Hardest part is finding a venue.
Some places to think about when starting to find venue space:
Your school (gym or cafeteria)
Local college (gym, cafeteria, or other space)
Church/place of worship if you are religious or know someone else who is
Library
If you are a scout (Scouts BSA, Girl Scouts or other youth organizations are usually connected to a place, like a church or a school that you may not even go to)
This list was created with the idea that you are somewhat young. Also, I am 14 years old, and I am organizing a competition with the help of another person, so I wouldn’t worry too much about age. You seem like you can make reasonable decisions, so I would contact someone who has already organized once or twice at least and have them help you. It can be a daunting experience, but a fun one.
A quick word on venue pricing: 500 hundred dollars sounds like a lot, and it is, but usually that is doable. You can probably go as high as $1200 for the venue depending on how many people sign up, and how big the community is in Arkansas.
Hope this helps!