You can show her in the Household Pet category. She must be at least 4 months old to enter a show and she must be spayed by the time she's 8 months old if you want to continue showing her.
I'm most familiar with CFA since I've been showing my HHPs since 2008. You can find information about showing Household Pets on the CFA website.
As long as she is altered by 8 months and is never declawed, the household pet (also known as companion cat) class is perfect for her. Start bathing her every few weeks to get accustomed to a beauty routine. I have never gotten bitten or scratched b/c my cats were trained to tolerate the baths and blow drying + being handled in the ring. It's a lot of work but can be fun if your cat enjoys it.