If you're super crafty and have a power saw (I sure as heck don't XD), you could probably make a wooden hut by cutting notches out of the wood so they kind of slide together. It's called a dovetail joint if that means anything at all to you (I had to google it). That way, you don't have to worry about anything she can chew on that might be dangerous to her. Just make sure that _if_ you do this, make sure you don't use pressure treated wood, as the chemicals they use in treating it can be dangerous for animals.
Of course, don't make this if you don't feel comfortable using power tools, as I can imagine it would be rather dangerous for someone who isn't experienced in using them.