Check craigslist online and see what you can find second hand in your area. I think the idea of the curtain rod and a pretty curtain is great, but if you get a screen that has large panels on it (assuming it is cheap) she could possibly paint her side to dress it up with her art work and you could paint the other side to match your decor.
As far as what to get her for furniture, our children's rooms had a mattress/boxspring (got when they left the crib, low to the ground so no worry about falling out), a small book shelf and a nightstand or small short dresser (for clock, lamp, etc). We kept toys out of the room, but we also had an additional space for them to play.
Kids don't need much, but if it's a multipurpose room and you want to put the toys in it, look for a good second hand toybox and paint it pretty. We have one that was from my childhood. We use those big plastic buckets too. Kids have a hard time at a young age figuring out how to put everything away in lots of little places. We put all doll related things in one and most other things in another. Bookshelves are great for getting clutter up as well. We are huge book people so we have one in each kids room, full. When she's old enough to color, work puzzles and draw... you can get one of those fold away buffet tables that has an adjustable height. Another multi-purpose item. You can use it when you are entertaining or working on a project and it can grow with her.
Good luck. She will love having her own space, so no need to worry too much.
Liz
p.s. We LOVE those large wall stickers. One child has Tinkerbell and Ariel, the other has Dora and a couple of the Tinkerbell and Ariel ones too. They are about $15 a package and they can really transform a space. Lowes also sells large decorative stickers like huge flower shapes and cirlces. A fun way to jazz the walls up without any commitment or wall damage.