Definitely take Daz's advice about not getting a size that is too big for your daughter. My youngest son (9 yo), my DD (now 14) & I all study violin/fiddle. Our teacher has always been very protective of the kids not having violins too large for them. Practicing with the arm stretched out & the wrist curled around the fingerboard on a too-large instrument can cause tendonitis. I've had it from crocheting too much, & believe me, your DD doesn't want it!

As far as getting a decent instrument, I don't know anything about the bass, but I can tell you, trying to learn on a crap instrument is no fun. We try to balance this with the fact that kids are not exactly gentle with their instruments.

Good luck!