It's so great that you are protecting her!!
You might try fabric with UV protection to avoid the sunblock issue- there is something called "solarveil" - it's very lightweight, sheer, breathable) or perhaps buy the fabric and make your own sheet of sorts to cover your stroller. I also just bought a hat with a a really wide brim and UV protection for my baby. They have some hats that have extra fabric in the back to protect their necks, too.
I think your doctor may be okay with the sunblock on her face and hands, but I would recommend being careful with the hands since she may be putting them in her mouth. Perhaps you could also shade her with an umbrella while in the water. Of course this won't stop the reflection off the water, but it's better than nothing.