I am the mother of a 16 month old who made his first disney trip at 7 weeks and has been 5 times since, including trips at 3 months, 5 months, 9 months, 1 year and 15 months.
He can ride anything without a height requirement, which is most everything at DL and some things at DCA. Some of our favorites that the whole family can ride include the HM (he's not afraid yet), Peter Pan, POTC, Buzz, Mr. Toad, Pooh, TSMM, and Monster's Inc.
Additionally, the Nemo subs, Aladdin, Turtle Talk, Storybook Boats and Mark Twain provide great nap time for little ones as they are all very relaxing and relatively long rides/shows.
My little one also enjoys Dumbo, the Carrousel (he rides and I hold on to him in addition to belting him in), Flik's Flyers, Casey Jr., and the Heimlich train as they are very kid friendly rides. He also thinks that the Tiki Room show and Playhouse Disney shows are phenomenal, and he love, love, loves

the parades--especially the now defunct POD.
As for child swap, we use it for Soarin', Screamin', BTMRR, Space and Indy on a regular basis. It is also available for some other rides like ToT, the Maliboomer, etc. but either DH or I (or both in some cases) don't care to ride them, so we have never used them. For most child swaps you need to show the child and the person who is waiting to the CM who will then give you a slip of paper that you use to enter the ride after the first person has finished. The slip allows the adult who stayed behind plus one other person to enter the attraction either through the exit (Space, BTMRR, Indy) or at the FP line (Soarin'). I think that Screamin' uses the Single Rider entrance for child swap too.
Be sure to use FPs for the person who is standing in line to minimize your overall wait time. Also, get a FP for everyone, including the person using child swap, and over the course of the day you can build up a reserve of extra FPs. In the case of my DH and I, we always both get an FP for Space and then using child swap we can ride twice during the day on only one set of FPs!
If you are staying onsite or in the general vicinity of DL, be sure to take the time to go back to your room for naps and/or stroller breaks. Break time was/is especially important to us since DS was just learning to walk and didn't want to be cooped up in the stroller all day. We sometimes take him back to Toontown and let him run around in Goofy's house and garden to work off some energy, but the time back in the room is invaluable too!
Have a great trip everyone! Some people say that they would never bring a baby to DLR, but I have found that with a little modification to how my DH and I used to tour the parks, we have found that it is an enjoyable experience for all of us!