I rarely ever get sick and I never use Hand Sanitizer.
I'm the opposite. I rarely get sick but I use hand sanitizer by the gallons, LOL!
To the OP, try to teach your daughter to keep her hands away from her face. My oldest gets sick the most because she is constantly touching her face. Germs enter thru the eyes, nose, and mouth.
In Disney, we use sanitizer between every few rides and definitely before we eat anything. I also use disinfectant wipes on the table before we eat. Sanitize after touching menus before you eat. Menus are very germy, so are ketchup bottles, salt shakers, etc.
Also, I try very hard to not have our family share drinks, licks of ice cream, etc, so that if one of us picks up some bug, hopefully it doesn't get passed to others in the family. You are usually contagious before showing symptoms so we try hard not to share food while on vacation.
So far, we haven't had anyone get sick on a trip and we take yearly 2 week long vacations. We do drive so we aren't dealing with airplane germs, but so far we have survived Disney 9 times as a family and no illnesses.