Hello Kathleen!
I second everything Eoin said! The ferry companies run all year round, as people live on the Aran Islands. They may have updated information.
In the meantime, I had a look and found some B&B's and self-catering accommodations that might still be open in November, such as
Aran Walkers Lodge,
Aran Islands Camping & Glamping (until November 8 only) or
Tigh Fitz Apartments. I'd suggest contacting them directly to make sure.
If you still struggle to find accommodation, I can also suggest staying in Doolin (if you book a crossing with the Doolin Ferry Company), Galway or Rossavel (Rossaveal is the ferry terminal for Aran Islands Ferries but they also offer bus rides from Galway).
Let us know if you find a place to stay and talk soon!
Antoine