I totally understand your concerns about the vaccines she would need. But being my hubby is in the military, I have an understanding about why we have to have them. There are some things that your daughter could catch that would be way worse than the side effect of the vaccine for it. And there are some diseases that if a person caught it, wouldn't be allowed back in the United States. Do you know which ones you would need for where you want to go? I would highly recommend talking with her pediatrician about your travel plans and how long you plan on being away. He/She will know the best course of action to take in protecting your daughter from anything she could possibly come in contact with.
Good luck and have a safe trip!!