Soundproofing panels=wall.

You can't block sound with panels without sealing off the space. The sound will just wrap around them. A piece of insulation sitting on the floor does nothing to keep the house warm.

Could you put in glass instead of drywall? Will seal off the loft without losing the light. Pix would help. Can you post?

Tell your daughter that she can't use the loft as her bedroom because it's not feasible unless you build a wall?

Well I know this isn't what you asked, but are you entirely certain it needs to be "soundproof"? Or is that possibly an assumption you are making?

Where do you anticipate the most noise coming from? How old is your daughter? Do you have other kids? Is there another bedroom available to her?

I think my approach would be more parenting-based rather than renovations, assuming she has other options for a bedroom. If she is over the age of 8 I would explain to her that if she chooses a living space that is more open to traffic (ie a loft, or hostel, or rooming house, or sorority house) she will inevitably hear her housemates. And I would also explain to her that as good members of a community we need to be considerate of our neighbours and not be loud after a reasonable time of day (which in your house, you would define). Then I would let her move up to the loft with no alterations whatsoever and let her either succeed in the experiment or fail and move back to an enclosed room with a little more life experience. Maybe there will be no noise disturbances at all. Or maybe she discovers that she can sleep right through them (a useful trait in college). Or maybe she discovers that loft life is not for her and she never makes that mistake as an adult, when the stakes are so much higher.

If she is under 8 I might not allow this choice just because of the fact that I really do parent as described above and I don't think kids that age are quite developmentally able to consider all those factors.

If she is over 18 she is on her own as far as any renos go and I wouldn't do anything beside offering to install a curtain rod or two for privacy.

If there is no other bedroom available and/or my parenting style doesn't work for your family I think your least expensive option will be drywall. It won't be soundproof but unless she is planning to use it as a recording studio, soundproof isn't necessary.