Awwwww your resident "retard" looks like a gentle giant.

Tilly looks
lovely and if she enjoys your company and follows you from room to room I would think she's well on her way to getting herself accustomed.
I'm also a first time cat owner! We adopted our 18 month old Simba on the 8th.
You'd be surprised what she has in her.

Give her time and lots of company too! Maybe she will follow you downstairs when she feels up to it. Right now it's good that she has the upstairs to feel safe in.