Yes, and please consider that the baby is tiny, but the gear for the baby is not. Whether you bring a PNP or get a crib from Disney, add in a stroller and the rest, and I would have to think that you are already out of the running for a "room for 5 plus baby" situation. Those "sleeps 5" rooms look tight for five, and baby + gear would make them tighter.
If you think CL would work for you (if nothing else, you wake up and can get breakfast right there before heading out), those deluxe rooms could be OK. For a more affordable price, AoA suites and the Cabins at Ft Wilderness would work, too.
The Cabins are nice if your kids can make a ruckus as mine can, as you share a wall with no one! It lowered my stress level. The bedroom is tight with a queen and bunk beds, so you would have to figure out the baby's sleeping situation. But the living/dinning/kitchen area was roomy enough. My 2yo shared the sofa bed with the 12yo or squeezed in with us. The 9yo and 7yo loved the bunks and have asked to go back. And we all loved tooling around the grounds in the golf cart we rented. The Fort is really a special place unlike anywhere else at WDW. Deer, rabbits, green space that is appropriate for running around and playing, nice splash pad.
But AoA gives you two bathrooms and is on the Skyliner system, if you're looking at lots of DHS or Epcot days. And I give it the edge in dining options (including hours of availability).
I actually smiled just reading the title of this thread, as it got me misty for our first Disney family trip, to DLR seven years ago when my three sons were 8, 5, and 2. It's really a special trip when all are young, no one is "too cool" or has "grown out" (or been Disney aged out) of any experience. You will have a magical time (with lots of hand washing because if one gets sick, they can take you all out)!