Any rabbit can be shown at ARBA shows, however, if it obviously does not meet the breed standards, it is likely to be disqualified immediately.
I would ask myself these questions -
What breed is my rabbit? If you don't know, or if it's a mix, it likely won't do well at ARBA shows.
Is my rabbit tattooed? It must be tattooed in it's right ear in order to show at an ARBA show.
What age / how many litters has my rabbit had? Most show bunnies are fairly young - less than 2 years. Also, if your rabbit has had numerous litters, she likely won't show well. In some classes, you must know the age of your rabbit in order to enter it into the correct class.
Does my rabbit have any breed disqualifications, and does it meet the judging requirements? Across the board disqualifications are missing or mismatched toenails, malloclusion, obvious illness and obvious body flaws, such as missing ear, foot or tail. In addition, many breeds have other breed disqualifications such as color, ear length, eye color, weight, etc.
These are some things to consider if you are wanting to go to an ARBA sanctioned show. County or local fairs, 4H shows, etc, do not have many of the same requirements.
My suggestion is for you to go to the ARBA website
www.ARBA.com and do some reading. Also google the specific breed club that you believe your rabbit to be, and check out some of the breed standards. Finally google rabbit shows in your area. You should be able to find out the whens and wheres in order to get started. Attending a show will help to answer all of your questions. Good luck!