E.L.
When we switched our daughter to a toddler bed she stayed there at first (like she couldn't get out, like the crib) but then figured out her new freedom.
We tried the "Silent Return". I don't remember whose book it's from. You just take the child back to bed without ANY talking to them and little, if any, eye contact. Sometimes you may do it one after the other after the other. She'll hate it. Eventually our daughter stayed there. It also works best to have just one parent doing the "Return", so that they don't "test" the other parent.
You daughter is old enough to stay there on her own. You can help her learn how to do it.
Good luck!