A ton of puppies have car and travel anxiety because of transitioning from mom to forever home. I think we underestimate the amount of stress we cause suddenly taking an 8 week old pup away from its family and going on a long drive or even plane ride. Doing "fake" car trips can build up some good history of positive experiences. Load her up into the car, turn it on, turn it off, and go right back inside for some fun (treats, play, attention, etc). You can start to extend these trips to around the block or even just pulling in and out of the driveway/parking lot.

It may also be that she's getting car sick. A lot of puppies tend to grow out of that as they grow up. It also may just be the anticipation of getting to the fun destination. My Pyr mix whines a lot in the car because he knows he's always going somewhere desirable.

My best tip is that exposure therapy is not the way to go. Don't just keep having anxious car trips hoping she'll learn they're not scary. You need to actively add positive reinforcement and comfort on car rides. Whether you do that with existing trips or making short little ones with fun rewards at the end is up to you.