Transport h1n1 vaccine outside country?

Some of my family lives in USA and some live outside the country. My brother is a doctor. We both live in New Jersey. He's worried that my family who live abroad are susceptible to swine flu so he got me a little bottle of the vaccine and told me to take it with me when visit them this Xmas. So I would have to carry it on the plane with ice in a cooler box. My question is... am I allowed to do this? Will airport security say .. hey you! why are you taking this out of the country? My brother could write a prescription but it's still odd.. who gets a prescription for vaccine anyway? I am scared of getting into trouble..