There is no minimum age - ARBA rules only state that a youth must be able to handle their own rabbit.
For very young children, I recommend using a stool to stand on, and wrapping the rabbit in a towel and placing up on the side of the table if necessary (rather than over the top of closed coops). An open-top crate or basket can also be used to carry the rabbit to the table because it's easier for the child to get the rabbit out. Judges are generally very graciousin allowing the younger children to get their rabbits on the table any way they can (except for scruffing the neck or putting the rabbit's safety at risk). With the judges permission, they can also come behind the table to put the rabbit up and take it off. (Always ask first - ARBA rule prohibit unauthorized persons behind the judging table.)
Parents may only put the rabbit on the table if the rabbit is entered in open class.
Pam