You could also invest in one of the folding practice beams so she could have the opportunity to practice and become more comfortable. It is a great confidence builder for handstands, cartwheels, and leaps. My daughter was terrified of beam for part of the season in level 3 (after she took a painful fall) and part in level 4 (no known reason). She is (and has always been) great on the beam, and it is one of her favorite events at level 5. Who knows?
This year she has worked thru other fears on bars and vault. It is terribly frustrating to watch her be held back by fear, but she is learning to work thru it. As life lessons go, dealing with scary things is a good one. As one of the coaches in our gym says, most normal people would look at what these girls do and agree that it IS scary (even insane!).
Good luck! This too shall pass.