No, as a PP said, you cannot ride with your child.
As you can see there are differing opinions on this subject, and that is fine. However, like I said, when it comes to Disney, it is a different world. My daughter passes out at the dinner table with her head in the butter (I have pictures), and pretty much wherever we stop for too long of a time. I would rather have her less tired and able to enjoy more than to have her completely exhausted and miss a lot on the trip. Plus, I refuse to be one of those parents I see on the bus that has carried their child a million miles b/c they passed out, or one of the ones dealing with an overexerted, overstimulated child throwing a fit at the end of a long day. We've never had a Disney meltdown b/c we keep the kids well rested. My daughter is still small (not undersized, just a little girl), and trying to keep up with her older siblings would exhaust anyone's legs. I'd rather her be able to kick back when she needs to and take a nap comfortably, or just be able to rest her legs while we race to the next ride b/c that is what we love. I have been up in the air about taking it, but I would rather take it and have it than leave it at home and have to rent one if I find she is pooping out. After all, it is about her enjoyment. This is a child who has a heavy martial arts training schedule, and is very active, so that is saying something. She has the ability to walk as far as she has to, but why push her too hard if she can rest when she needs it. She trains hard all year, so this is her time to take it easy and enjoy her vacation, just as it is my time to make sure we have fresh, energetic children so I can enjoy my vacation as well. My hubby is a strong guy, and she's not that heavy, plus my stroller corners like a champ! So...you will get strong opinions, but you have to do what works for you, and my back going out from carrying a sleeping child does not work for me. No one has ever judged me at Disney, only on the boards, so don't worry about people giving you the stink eye. I can't help with cost as I bring my own.
As for a picture, I was able to pull them up on Google images pretty easily by typing in "Disney strollers".