My DS went from kindergarten to 2nd for math last year. He did just fine as a 6 year old with kids on the cusp of 9. Just Fine.
Honestly, if your DD has a lot of talent for each reading and math, then 2nd is likely the right place. 1st grade was a lot of making sure those skills they hoped kids would get in kindergarten actually got learned. When I visited the 1st grade math class mid-year to weigh in on where I thought DS needed to be, the class was still working on number patterns 1-100. Things like adding 10 to a number leaves the ones place the same. Things like knowing that 46 is bigger than 37.
As I recommended to another poster here recently, ask for a transition plan. This is part of what I think made DS so successful last year. It was put in writing who was going to escort him to the 2nd grade class and for how long (2 weeks), where homework was going to be, how he would be taught the new classroom routines (like how to announce he needs to use the bathroom), who he'd sit with, the frequency with which the teacher would communicate with us, the form of feedback, and how the kindergarten teacher would adjust his day so that he got the instruction he needed from kindergarten. Everything was overseen by the vice principal, so all communication was cc'd to her as well. She observed him 2-3 times in the first two weeks as well.