Mine left her next to me crib months ago. Night 1 in her space saving cot wasn’t a great success but that’s what she needed to sleep in. She’ll be in her big cot as of Jan and likely that’ll take some transition too as it’s really big.
It takes a while to get used to the bigger space, lots of playing and chilling time in the cot during the day should help but she will adapt in time x
If she isn't sitting up on her own yet, it may be worth getting a next2me cot as they are much smaller than a regular cot but bigger than a basket. Failing that, it could be worth getting a "sleep nest" for baby to lay in inside the cot so they feel a little more secure while she gets used to being in the cot x