If you were planning on attacking the parks "commando-style" (up early, run all day, stay late, repeat), I'd say that seven nights would be too much for a six month old.
However, by your signature, I see you've got enough trips in your past to afford to take it easy. I would think you could take your time and be OK with planning your days around your little one. Be prepared for nap times, maybe not sleeping through the night so a late start and many, many breaks. In January, weather and crowds should not be a major issue.
We've been to WDW when my daughter was 15 months and then again when my son was 12 months. We had a great time, but it was not the same trip as without them. You just have to let their mood guide you.
Of course, you'll have grandparents there to help as well. Use those Fastpasses wisely and don't forget the babyswap! In my experience, the baby swap was good for at least those sitting out and, in at least one occassion, for up to six people in our party!
Have a great time. Congrats on the baby. Good luck with the grandparents. And if you still think seven nights at the Polynesian will be too much, I'd be happy to take your vacation for you!