Hi and Welcome to PT.

The fact that she's hiding and not eating much I would think, suggests that perhaps she's afraid of being 'exposed' to the dog while she's at her dishes, she may feel it's not safe to be out there.

It sounds like to me that the 'introductions' were too fast for her.

What I would do, is put her and her dishes somewhere where the dog cant get to for a few days, somewhere where she can feel safe, that includes the litter box, hopefully she's using that. After a few days (you have to go in and spend time with her though) leave the door open, and see how things progress.

It's not good for a cat to go without water/food for an extended period of time. So make that always available to her wherever she is.

Good luck.