When my DD was about your DD's age, we went on a cruise. I also packed about 6 diapers for each day and put an additional 10 or so in our carryon diaper bag for good measure.
As for clothes, I brought a lot (2 outfits per day) because DD was still spitting up at that age. Besides, their clothes are so small that it hardly added anything to the suitcase. One bottle of sunscreen should be plenty. Also bring a hat (their little scalps burn easily)and one of the sunscreen sticks for your DD's face.
For an 8 month old, definitely bring tylenol, Hyland's teeting tablets, and Oragel. At this age, you never know when they are going to pop a tooth. My poor DD popped FOUR teeth the week that we were on the cruise!!!!
If you are worried about overpacking, keep in mind that the Baby Care Centers carry most of the items that you would possibly need, but you will pay a big premium. Personally, I prefer to overpack and know that I have more than enough of the essentials.