She'd probably be less anxious at home where it's safe & familiar than in the back of the SUV. Think about the traffic sounds, people pulling in & out of the parking lot, and her wondering what's going on around her, all while she's somewhere different.
Play with her alot before you leave & tire her out and she'll most likely sleep the whole time.
Good luck with your dress shopping. Enjoy the day...it's a memory you're creating that you'll look back on forever