There are plenty of rides that baby can go on, plus they have a baby swap, where one parent goes on and then the other goes afterward. If you have additional kids that are big enough for those rides, they usually let those kids ride with each parent!
In DL the baby can go on all of the "dark" rides - Pooh, Pinocchio, Snow White, Peter Pan, Alice and Mr. Toad - IaSW, Storybook Train, DL RR, Jungle Cruise, PotC, HM.
In DCA, you have shows - Aladdin, Playhouse Disney, Muppets and Golden Dreams - Bug's Land Rides, Ferris Wheel (non swinging side) and Monsters Inc.
There's a lot you can do with a baby. I would suggest bringing both a stroller and a baby carrier (like a Baby Bjorn). Also, there is a Baby Center in each park with rocking chairs. In DL it's just before the circle on the right side of Main St. In DCA it's in the back of the Mission Tortilla Factory.
Have fun.