I have a similar problem, not seperation anxiety, just center of attention constantly. I'm due mid february a friend of mine suggested I try givin my dog one of the first receiving blankets the baby is wrapped in, because then he can get the smell bfore he meets the baby. My mother also says we will just have to alternate giving him attention while the other hklds the baby. I don't have any kids yet so I dunno how well these will work, but thought I'd pass it on and you can try it as well!
Also, I forgot.to include, the friend that suggested the blanket thing, had another friend who actually did that and apparently it.worked. In my experience though a pets are different, and have different temperaments, my dog for example is very loving and protective, and is like that with anyone who he is close with so I blieve once he gets used to the baby he will be fine. I hope you have an easy time with it
I had a puppy when i was pregnant with my toddler! She was also very spoiled, i shared my food with her, she slept in my bed with me she had her own clothes and used to go everywhere i went. When my daughter was born i had no issues surprisingly. The dog was actually very protective of her and threw a fit if someone took her out of sight. :)