From what I am reading I think if you live in Texas you are out of luck. Here is a link to a website that has some great information:
States Allowing Medical Exemptions for Rabies Vaccination | Truth4Dogs
I don't know if airlines would except titer tests but I did read somewhere that some countries require titer tests and the dog has to have a microchip so that the titer test can be matched to the dog.
Did you take the her back to the vet? You might ask your vet about the exemption and the titer testing. Hopefully she will heal quickly and the hair will grow back.