You are going to get tons of advice telling you to skip. Above all else, I think you need to trust your own mommy gut instinct and your DD's judgment/preference.
In my opinion, it is okay to not grade-skip your DD. While I am not inclined to share horror stories, there have been several double-grade skips in my family and with hindsight (college & beyond), I can honestly say that the landscape changes over time and the ledger of advantages/disadvantages shifts. Consequences are not always forseeable and individual experiences will vary.
My DS10 is a DYS and in fifth grade. A number of school personnel had mentioned grade skipping, but that wasn't what I wanted for my DS and also not what he wanted for himself. Back in 1st grade, he read 5th grade fiction independently (higher non-fiction as is typcial). As for math, I didn't bother assessing him in 1st grade but he tested fine with 5th grade math as a second grader when we underwent the process of subject acceleration in math. DS was accelerated to 4th grade level math in 2nd grade and then accelerated to Pre-algebra in 4th grade and is currently studying Algebra through an online course with a one-day a week teacher provided by the school district. From 1st through 4th grade, he was in the gifted classes, which use materials at least one grade above as well as novels to supplement the standard textbooks. His 1st grade teacher had bookcases full of 3rd/4th grade books due to previously teaching 3rd grade. DS probably read through her whole collection due to finishing his work early.
This has worked for my DS so far. He is well-adjusted with no emotional or behavior issues. However, it is important to note that neither DS nor I limit or defer learning to school. He is an avid reader and gets most of his reading material through the public library or purchase. While he uses the school library, its selections are clearly limited. The internet has been a great source of learning as well and he has had his own laptop for a couple of years. Many families have successfully avoided skipping also by focusing time/mental energy on the arts, music, chess, sports, etc.
Please note that I am not advising you not to skip. Only you and your DD can make the best decision for yourselves. However, you also should not feel pressured to skip.
