Hi there, Tracy!
My family is here at
Walt Disney World with my grandson right now, and I can share our experiences with you, because it has been a bit varied. I will say just to play it safe, you may want to go through the bag check area, although they may just wave you through.
On our first morning, my son-in-law took the baby in the stroller through the no bag area, but was stopped by security, who asked him to have the stroller checked. There was a baby carrier in the basket underneath, and it may have been that it looked enough like a bag to warrant a check. On our next park day, we went right for the bag check line, but the security guard there pretty much waved the stroller through. My daughter had put the diaper bag up to be checked, so that may have been why, but they never looked in the stroller basket at all.
Then yesterday, we took the stroller through the bag check line. Not only did they check the diaper bag, but they had us empty the basket in the stroller as well.
To avoid having to go back to the line, I'd say if you have anything at all in the basket of your stroller, you might need to hit the bag check line. If you have absolutely nothing, and it's clearly empty, you may be able to go through the no bag line with the stroller.
Have so much fun on your upcoming trip!
Anna