Originally Posted by TuffToodle
Is it possible for her kindergarten teacher and myself to "catch her up" enough this year so that next year she would be prepared to enter the second grade instead?
To manage your expectations, it would be unusual for a school to require a kindergarten teacher to prepare a child to pass the first grade end-of-year exam as prep to skip 1st grade and go to second grade.

You might want to read several old discussion threads on the pros-and-cons of acceleration.

Originally Posted by TuffToodle
Should I ask for first grade exit exam at the end of summer and let that be my goal for her GIEP?
IMO, your goals should be prep for interfacing with the school:
1) Read up on everything provided in the links, and feel calm and confident in your advocacy skills.
2) Have many conversations with your child and spouse and/or child's other parent. Your family must be of one accord.
3) For your first meeting, practice listening, taking notes, asking questions, learning how things work at that school.