@Penelope4, what an unfortunate occurrence. You're right about adding insult to injury. Sounds like the guest is trying to avoid you.
Because you required no Security Deposit, you won't be able to claim for the damage. However, I would suggest that you contact AirBnB right away and tell them what happened.
In fact, she has already broken one of your House Rules (which I assume were in place when she booked).
Perhaps you can be compensated via the Resolution Center.
Here's a useful thread/link.
https://community.airbnb.com/t5/General-Hosting/The-Resolution-Center-A-Community-Help-Guide-Request...
For the future, I strongly recommend you set a Security Deposit amount. I also advise having a more comprehensive and firm set of House Rules. You could mention, for instance, that the antique canes are for a decorative purpose only, and are not to be removed from the umbrella stand.