Our cat was very interested in the bassinette and cot.
I had the bassinette in our room form about 3 months so she would get the boot, didnt take her long to figure it out.

When we got the cot up a couple of months before we had DD the cat tried it once, then got the boot again and she got the idea.
After charlotte was born she didnt want to go near her! lol too scared I think hehehe. Even now she barely speaks to Charlotte (is not very patient with kids, Miss Moneypenny! lol)

Anyway, we found that by having things up early and establishing that the cat was not allowed even in the nursery or in the bassinette, we were fine.