Hi There, This Morning I Drove Over A Dead Dog

Hi there, this morning I drove over a dead dog in road with my car. If the dog had rabies and some of the spatter (blood, saliva, brain tissue) got on my car door and I touched my car door, can I contract rabies?
I have some cuts on my hand from doing lots of dishes as well as eczema. Please advise, freaking out!

Regards,
Suzette