Hi, Marlee! I'll tackle the easy parts first! Yes, there are strollers available for rent at each of the theme parks. A single stroller will run you about $15 per day, and you can find all the information you need on stroller rentals by checking out this link
Disney World Stroller Rental. You may find that the strollers you can rent are a little less comfortably for a seven month old than what you're used to. There is a stroller available for purchase at the parks that runs less than $60. It's a little more comfortable for younger children, and you can take it back home with you using the gate check option. You could also bring one from home, and gate check that as well.
Each theme park has a Baby Care Center, and there are well equipped rooms there for nursing. You'll find rocking chairs and a comfortable, air conditioned environment where you and your tiny one can relax.
As for the must see things, that varies by person. Some of the most popular attractions include Pirates of the Caribbean, the Haunted Manion, Space Mountain, Splash Mountain, and Buzz Lightyear at the Magic Kingdom. EPCOT has Soarin', Test Track, and Maelstrom in the Norway Pavilion. At Disney's Hollywood Studios, some of the atractions that are not to be missed include Toy Story Midway Mania, Tower of Terror, Rock 'N' Roller Coaster, and Voyage of the Little Mermaid. Don't miss Expedition Everest, Kali River Rapids, or Kiliminjaro Safari at Animal Kingdom. And if you aren't too tired, stay for the night time shows at each park. Wishes at the Magic Kingdom is stunning, Fantasmic! at the Studios is amazing, and Illuminations at EPCOT is inspiring.
Have a wonderful vacation!