Every time I hear about girls doing OK socially after a skip, it seems they are tall for their age and or, their birthdays were not so much past the cut-off.
FWIW, my DD has a May 31 birthday (September 1 cutoff). She was not the youngest in her class before the skip, but was at the young end. Many of her 3rd grade classmates are 18 months older than she is.
She's also about 50th percentile height-for-age. She was very concerned about being the shortest kid in the older grade, but most kids are slowing down some in growth as they hit 8 and 9, so you don't have to be a particularly tall 7yo to avoid being shorter than the smallest 8yo. If your DD is already significantly shorter than her age-mates, she's obviously going to be significantly shorter than kids a year older, but it won't necessarily be as big a difference as you think.
DD doesn't even come up to the shoulder of her (very, very tall-for-age) best friend. She's been just as socially involved (in terms of party invitations and playdates) as a 3rd grader as she was as a 1st grader, and I like her friends better this year than I did last. Her first-grade friends tended to be low-average performers in school. Her third-grade friends are much smarter - they recognize DD as being smart, but not so smart that they feel outclassed, if that makes sense.
I had my concerns at the beginning of the year, but the skip has been a good social move, as well as a good academic move. I'm sure that's not always the case, but I thought it might be helpful for you to hear an anecdote from the other side.
