You’re absolutely right to be cautious. I am a huge dog lover, have two myself but you really do have to be careful when dogs experience big changes their temperament and behaviour can change. My cousin had her baby and two of them moved out all around the same time and the family dog completely changed. He was quite aggressive at times around the baby (something which he wasn’t before!) and extremely jealous of my aunt. I guess you just need to make sure you’re giving your dog just as much attention and love as you did before and correct any bad behaviour
My dog paws at me when I nurse my son on the couch sometimes. I'm trying to make sure that she gets some one on one time with me to help her feel less jealous, so we are going on some solo walks without the baby and I am scheduling playtime with just her and I every day. She's a big Mama's girl so I figured she would find sharing me a little hard. But we are also practicing the behaviour we want to see from her instead. So not giving her attention when she is demanding it on the couch, and rewarding her with attention when she acts how we would like her to, such as laying nearby and being patient.