Please, please, please vax your little one. A free car seat won't do you any good if you're spending all your time in the hospital. Or possibly worse.
But if you guys have legitimate concerns, like a family history of certain allergies (I know they mention some people with egg allergies have to be cautious with the MMR, for example), then this is something you guys need to discuss with your pediatrician to see if you can split up certain shots. It will involve more visits, but at least the kid will be getting the protection she needs.