Is it safe for me to drive my baby around in a small car, even if I keep her in the back seat?

Car seats! Properly securing an appropriate car seat is vital to the baby's safety. Safe driving practices are obviously essential too! The size of your vehicle is a factor in car safety as well, but this is not specific to your baby.
That depends. The relative safety in any vehicle depends on many variables. If baby is placed as far from potential crash forces as possible (preferably the middle of the back seat) in a proper seat; you have done the best you can for the vehicle you drive. If the car has enough room for a good seat instalation I consider it safe. The little vs big car vulnerability is basic physics & the same for you & baby.