I was once in the meds isle at one of the gift shops, and a clerk also told me if there was anything I needed that they didn't have, they could get it delivered for me. I didn't end up using the service, but they said they could get anything delivered, even prescriptions if needed. I didn't find out about prices though.
Another place that has some baby needs/meds is the child care center/nuse's station in each park. I once needed Benadryl at MK, and they had all kinds of basic meds available in travel sizes. Maybe not the ideal prices, but it can be had.
If you have a car, there are lots of places around too. Like 24hour Walgreens; they're all over Orlando.
Also, right near WDW, off I-4 is an outlet mall where you can pick up lots of items. My sister once had to buy new sneakers shortly after arriving. Next to the outlet mall is a Publix grocery store. There's also a
Walmart in the area. If you really had to, it would be pretty easy to get a taxi over to one of these, too.
One thing I've discovered is that moleskin is a very useful thing to bring to WDW. It has lots of uses.