yes, i would say do it.
you and her are close, and going out of your way and putting in all that effort will definitely cheer her up. since you guys are close theres no way shed reject it either. she wont think your jsut trying to get in her pants either because guys who are trying to do that would usually be the ones who would not invest effort in it. But she would realise and appreciate that you put in a great deal of effort just for her out of your own will just because shes feeling crap.
shell love it.
you could frame it if you want, however, i would just stick it up on her wall and dont make to much of a fuss about it, like it would be the natural thing for you to do. then shell frame it her self if she wants, which she probably will, because shell want to make sure that it stays safe.
but good going anyway mate, a girl will always appreciate when you go out of your way to do something like that because it has alot more meaning than simply going out and buying a giant sideshow beany tiger and will hint to her that you do like her. but if she doesnt feel the same way then it will just look like the act of a good friend. so either way, nothing will be lost and you can only gain.