I don't really AP but I remember DD1 was like this from 12 weeks to about 8 months! She wouldn't let me out of her sight and didn't want to go to anyone else. She suddenly snapped out of it and has been fine ever since. DD2 was fine until 9 months and now she has started - I hope it doesn't last as long for her.

I don't think it is "usual" as such but it is not uncommon to have separation anxiety at a very young age.