What FJM said. Every bit of training with dogs is about desensitization and acclimatization. Take it slow and don't rush it. One or two sessions per day, and only progress when she's ready. I find it helps to write down what you think will be the incremental steps (reality often changes things):
Step 1 - get in car, treat! When she's eager to get in the car, go to the next step:
Step 2 - get in car, treat in the carrier! When she's eager to get in the carrier, go to:
Step 3 - get in car, get in carrier, start the car, while the car is running, treat! When she remains calm with the car running, go to:
Step 4 - get in car, get in carrier, start the car, roll down the driveway and back, treat! When she remains calm, go to ... drive around the block, a 3 minute drive, a 5 minute drive, a 10 minute drive, a courtesy vet appointment (many vets, knowing that dogs hate vet appointments, offer a service where they will pick up your dog, bring her in for a treat, coo over her cute little self, make sure she had a good time, then send her on her way), a fun trip to a park,....
If at any point she doesn't seem calm with the current step, go back down to a step where she is calm.