I've taken babies/toddlers to WDW, but not as an "only"--the trip was meant more for older children, with the younger one tagging along, if that makes sense. I would probably not choose to take a baby/toddler to WDW, especially as a single parent, since your DH doesn't want to go.
That said, a lot of people certainly do take very young ones, and have a good time doing it. So, if you want to go, and are aware of the limitations (some rides off-limits, schedule will be the baby's schedule, etc.), you'll probably have a nice time. As someone said up-thread, though, a lot depends on the child's temperament. If you have an easy-going kid, you should be just fine.
The one thing I think you should really think about and plan for is, the logistics of being a single parent on this trip. I know you're meeting up with your mother and sister, which will hopefully be a big help, but the baby might not take to them right away, especially if she doesn't have a lot of familiarity with them. I also think the idea of flying down solo is going to be logistically tricky--do-able, for sure, but just make sure you think it through, plan for any contingencies, etc. Personally, I'd buy the second seat and bring the car seat--it allows for a familiar spot for the child, as well as giving you a bit of a break. You should be able to gate-check your stroller. Think about juggling your baby, stroller, carry-on--might it be worth checking your luggage? That's just the type of thing you need to think through, way prior to actually boarding the airplane. Similarly, are you getting your own hotel room, or sharing? Would sharing work for the child you have?
Don't misunderstand--I truly think you can have a great trip, I just think that's it's going to be a different type of trip than you're probably used to.