DD2 was a climber also which she never grew out of.
We had big boxes with areas cut out, like a cubby, which they had to climb in and out of and this helped a bit. Maybe one of those tunnels would be good.
If you can afford it get her something that she can climb or hang from for Christmas, a swing set with a hanging thing is good.
By the way, a natural climber hardly ever falls, it's the others who think they can climb like your DD that do fall.