I would think long and hard before I moved my child up a grade. There are social considerations to make, not just for now... but say, when she is 14. All her friends (15 yrs old) are dating... are you going to let her? She's going to want to date someone the next grade (or 2 grades) up at some point... that'd be 2 or 3 yrs not 1 or 2.
Ask the front office at her school, and her teacher if they don't give you what you need, for paperwork to request application to the gifted/talented program. Our school doesn't have AP classes until 6th grade. But gifted and talented starts WAY before that. Usually they must be referred to the program by 2 sources (1 teacher and 1 para, 1 teacher and a parent, a parent and test scores, etc). Also, our school requires that a student be in a teacher's class for like 6 weeks or something before the teacher is allowed to refer the child. (For adequate observation I guess).
In the meantime, challenge her in other ways. Enroll her in a weekly music lesson (piano? guitar? violin?), or a martial arts program (year round, not seasonal like soccer and it involves more than physical activity), or find a way for her to study a foreign language or take a weekly art class (not playtime, but an actual art CLASS where they learn ABOUT art and also do art).
Added later:
I went back and looked at my daughter's test scores from when she was younger. Her 1st grade scores (done in early April of her 1st grade year), showed her at grade 3.9 in one area, but her end of the 2nd grade SAT testing (also done in April) showed her reading skills(broken down in different categories) as grades 11.9 and PH (post high school). Maybe she didn't test well in 1st grade. Maybe she got lucky in 2nd grade. Maybe both. Who knows? What I do know is that she was later tested for gifted/talented and they admitted her immediately, and that either way, she is not emotionally/developmentally ready to spend all her time with kids older than herself. She needs her emotional peers as well as intellectual peers. And she has intellectual peers via the gifted/talented program, older brother and family and friends outside of school.
Her present teacher (4th grade this year) works very hard to continue challenging the students in her class that are able to move ahead and not keep the whole class waiting to learn new concepts in math because of a few students who need more help. She really tries to cater to students' needs.. not ease of work for herself. Some teachers are not able to accomplish this, others aren't motivated to do so, but some of them can and do. Just know that less than 2 years "ahead" of the norm language skills does NOT mean that she needs to be moved up in grade. A LOT of kids are ahead of the norm. Just like a few are behind the norm. The norm is formed from a compilation of scores, like a bell curve. MOST kids will fall somewhere close to actual grade when tested... 2.1 if tested the first month of school in 2nd grade, for ex. If she were reading at grade 6 then that is a much more dramatic difference. 3.9 is wonderful, but doesn't necessarily demonstrate a need for her to be challenged beyond the rest of her class.