No car, no car seat.
I would only consider it if you use the car seat as a place to but the baby for rest. At 7 months many babies like sitting up more then a infant carrier provides so I would not bother with it. If you think you will use it in the room as a place to rest or part of the stroller then bring it.
I have been to WDW 3 times with a child under 12 months old. !1st DD went at 8 months old. 2nd DD went at 7 months old, and again at 9 months old (got to love DVC, AP's and cheap airfare.)
As far as strollers go bring what you and child will be most comfortable. They do have smaller travel strollers that have most of the comfort of big graco even flow system strollers. We have a combi that folds up as small as a umbrella, reclines, has cup holders and a good shade. We used that for many WDW trips, it served us well. We also used an back pack stroller when 1st DD was a baby and it was great for us. We could change it from back pack to stroller with out taking her out and is very small. It does not recline, but she was able to sleep in it by leaning on the padded rail. She loved it.
Now my number one baby advice is get a stroller rain cover no mater what stroller you bring. It may or may not rain, but if it does you will be thankful for it. Bring a blanket almost everywhere. You can use it to carry in rides to keep baby warm in AC and dry from squirting water. Cover baby while nursing, or resting in stroller to keep light off. Also it is comfort from home. With a baby that age get some chain links and attach some toys to the stroller so they don't throw them.
Have some sort of baby carrier option too for lines and places where you don't want to be taking the baby in and out of the stroller too much. We used a baby bijorn. A sling works good too, there are lots of options, but get comfortable with it ahead of time.
More baby advice then you asked for, but there it is.
Best of luck and have a good time. 7 months is a great age to take a baby to WDW.