I wasn't packed at all and my first baby decided to appear at 36 weeks.
I was running around at midnight, in labour throwing everything into bags.
Of course I forgot half of it in my panic so my mother and DH were bringing things up the whole time we were in hospital My mum also spent those three days washing baby clothes and setting up her room because I hadn't done that either ...oops.

After that experience I was ready to rock with my son by 32 weeks - bags packed, nursery done, clothes washed and in drawers, and freezer full of food.
I didn't go early with him but I felt much better knowing I was organised.
So no, I don't think it's too early