I definitely agree with above poster. Having 10 nights will give you the time to slow your pace down to the baby's if need be. Both of our girls have been going to WDW with us since they were very small (my youngest started off at 4 months, and we drove from NJ that year and spent 2 weeks)and we have always tried to make the trips longer when they were small to allow us time to do what we want to do.
I guess the main concern is napping at this age. Definitely bring a good reclining stroller and any comfort toy the baby likes and maybe you'll get him or her to take naps during park days. Try to scope out a quiet place and it is possible. We have always had good luck with that. If the baby is not a "stroller napper", maybe one of you could go back to hotel during naptime with baby while other stays with your older daughter.
Explain to your older daughter beforehand that you'll want the baby to enjoy WDW too, and that might mean going a little slower through areas the baby likes, i.e. maybe going on Small World a few extra times or whatever seems to catch baby's attention.
There are great baby care centers all around the parks. Maybe you could find their locations on the Internet before you go down so you'll know where to go. I love the one off Main St. in MK...it is so quiet and gave our girls a break from the craziness sometimes.
Good luck and have a great time! Make sure to take lots of photos with baby & characters. They'll be very precious to look at years down the road!