She is 5 months into K and already scoring like an average to high second grader. It isn't as though she is going to make no progress in the next 9 months. At this point, with the skip, she is probably going to walk into 2nd grade already knowing much of what they are going to "teach" her there. The point of school is not to prove what you already know, it is to learn things you don't know yet. From the standpoint of the child who is going to be sitting in the classroom, spending 7 hours a day going over boring stuff already mastered is just torture. You don't want her to spend first grade hating school. K to 2 is one of the easier skips to make, since so much of the first grade curriculum is just basic reading instruction and simple addition and subtraction.
You have nine months to play writing and grammar games with her if you are really worried that her skills there are below par - but it might be good for her to have a work a bit and not be the best without even trying in some area.
She is already part of the social group that will be in 2nd, so there is no worry about not fitting in or not having friends.
I'm not seeing a single reason to argue against the grade skip. If this were my child, I'd go for it.
Does your school use the Iowa acceleration scales? Using this can often put it out there in black and white a lot more clearly and relieve some of the anxiety about whether you are doing the right thing. If you did use this tool, I think she would be rated as an excellent candidate for a grade skip.
