Not a good idea. If she is already a level five she has all her basic skills, you do not want her practicing level5/6/7 skills alone on a bar in your basement. She could really hurt herself, more likely though is she will develop skills with bad form and have to relearn them.
If she wants something to work on at home a pull up (attaches to a door frame) bar can be good for working on her strength and conditioning.
Though I do know that kids will swing on anything they find, a bar in the basement is a little different (especially one like you mentioned that she really could do skills on) as it will always be too tempting to her.
How about a nice beam?

Just my opinion...