I entered my quilt in Aqs Grand Rapids and Des Moines this year. It was accepted I to both.
I did not make the quilt with intention to show it, just decided to enter on a whim. All you have to do for aQS is send pictures and the application. Easy peasy. It is worth going to their website for size requirements.
Other thoughts:
Don't put a hanging sleeve on until uou have the specific show guidelines.
Be prepared for high shipping charges.
Make sure your quilt is clean and totally pet hair free
No quilt is totally mistake free so don't beat yourself up. For sure the one I had accepted is not.
If you want to win, your binding probably does need to be perfect. And 99.9% of the rest of it.
If you are doing a traditional design, it needs to stand out somehow to get ccepted. Be different if you can.