Moses basket at night

It's obviously your choice but really not recommended to leave babies unattended with pets, and that means when you're asleep too. Not because your dog is nasty, I'm sure your dog is lovely, but they can knock over moses baskets or sit on your baby without knowing they're causing harm... it might be a good idea to transition your dog out of being in the room - if not, no worries!
As long as she is in the room with you and you comfort her and tend to all her other needs, she will know you're there and not be negatively affected.

I think you need to put boundaries in place. Your dog has crossed the line, knowingly or unknowingly by jumping into the moses basket. Before I had my little one, my dog was my baby and although he slept downstairs, he used to spend the majority of the day upstairs on the end of my bed while I worked from home. Understandably, he has struggled with the transition but the whole of upstairs is now a dog free zone. I need to be able to put my baby in the cot and go for a wee at least without worrying about my dog being there! I'm sure your dog is lovely but dogs can turn at any point and I would not be comfortable sleeping while a dog and a baby are in a room together, without someone else being awake, alert and in control. X

I also have my dog in with us at night (but she quite often sleeps under the bed) and it took some time but she has become less interested in our daughter so doesn’t really try and investigate where she sleeps now. I think it’s easier said than done talking about getting the dog out from upstairs, if I had to do that my dog would cry/bark which on top of a newborn baby would be very hard and equally agree you can’t change too much for them, in turn you could make your dog unhappy which would then affect the way they act towards the baby.
I see you say about a moses basket, have you tried a next to me crib? We initially got a moses basket for downstairs get felt it would be too easy for the dog to knock over. The next to me is really sturdy, the newest one released you can actually adjust the height as well x

Thank you all for your comments.

Unfortunately my dog suffers with separation anxiety so transitioning him away from the bedroom would be such a long process and I think would negatively impact his behaviour towards the baby. He's not fussed by the baby at all and when she's in her bouncer or tummy time ect he isn't bothered and will curl up and sleep - so the fact he jumped in there really shocked me.

I appreciate all of your comments - I'll look into a next to me crib and also will attempt to train the dog to come away from the bed and back to his own! Having a fur baby before an actual baby meant he got away with anything!🙈

Not a dog but my free roam house bunny likes to try and get into the basket and bouncer. I never leave them unattended together and upstairs is now out of bounds so baby can have tummy time and sleep undisturbed by an inquisitive rabbit.
He's very cute with her and comes to the side of her crib when she cries or puts his head on her belly when they're both on the floor, I'm not worried about him intending to harm but the risk of suffocation is too high.