A common method of bike sizing is to multiply the inseam by .65. For your daughter that would be 32cm as the nominal frame size. In her case, the bike size should allow the saddle to be adjusted in a relatively low position when her heel is on the pedal and her leg is straight, to give her room to grow.

Perhaps the best way to increase confidence on the bike is to lower the saddle all the way down and take off the pedals and "stabilizers," maybe even the chain. Have her propel the bike with her feet on the ground, so a push bike. She could probably do that with her current bike. In fact the best way to start a child on a bike is a push bike. They can start on one as young as 2. When we bike toured in the Czech Republic, it was very common to see a family on the street, sightseeing or shopping, with the small children on push bikes. Made it easy for them to keep up with the adults and not tire, plus they're easier to keep track of that way.