I'd second Kmn's idea - shift the particularly heavy climbable furniture into your room if there's space, or a spare room where the door can be closed for peace of mind. They do eventually grow out of it, or at least redirect the climbing to playgrounds and such like - give her plenty of opportunities to climb in ways that are acceptable.

Funnily enough DD's favourite thing to climb when she was at that stage was my bed. Massive 4 poster with an ensemble on top so it was high enough that I had to half climb up into (and I'm 5' 11" tall) it must've been like Mt Everest to her...