I hadn't even thought of adolescence being a potentially awkward issue for OP's dd -- isn't it odd, 'earlier' development of adolescence for a boy (per his peers) is considered a bonus, but not for a girl?
Although I agree that's the case in our culture, it sure seems sad.
My aunt put her oldest son in school 'on schedule' (he was a July birthday, cut-off was late August). He struggled, and was held back in the second grade. Frankly IMO his whole life has been impacted by being in school before he was really ready; she felt that he wasn't ready at the time, but had a lot of pressure to put him in (he was her oldest, too, so I think she was less certain about bucking the status quo). She held her second son back a year, even though he was a March birthday I believe. And she and he are both happy about that and feel that it worked out well. She said he just wasn't 'ready,' to sit down and focus and do all the 'school' tasks.
I'm glad both my girls have early fall birthdays - they don't meet the cut-off, they will naturally be the 'oldest' in their classes (we homeschool right now, but if/when they are in a brick and mortar school - certainly by college). I've always hoped that means that they will be a little more emotionally mature than their classmates, a little more able to insulate and negotiate some of the pressures and decisions of the social structures of school.
Finland doesn't start school 'til kids are 7 years old (formally). Yet they are top of the world for test scores/achievement by their students. SO -- personally I feel that there's no rush to get a kiddo into a school setting. You can unschool at home for a year (go ahead and tell people you're homeschooling if you are feeling a lot of pressure). I think that, with the possible exception of foreign language, an attentive parent can help a kid learn at home for the basics that they need before they start formal school -- alphabet, phonics, numbers/math, some very cool science and history things just as a matter of course - art, music. There is a lot of research which shows the facility of starting a foreign language before or at Kindergarten age - but since that's really rare in most American public schools, it's not like your dd would be missing out on that. I have a friend whose boys are in a German immersion school since Preschool, but I think that's an exception, those sorts of opportunities are unlikely.
The reaction that people have tended to have to Ina being essentially an "old" kindergartener have been:
1. Oh, she's so bright, you should challenge in! [My response: I like spending time with her, she's learning at home too, and one more year to be a kid before she has to be stuck in school all the time, seems to me like a wonderful bonus for her!]
2. Well, they'll figure out the emotional maturity thing - it just takes a few years to catch up. [This from my sister, whose daughter barely made the *next* year's cut-off for K, but enrolled her anyway. Her daughter is actually pretty advanced, even emotionally, for her age. So maybe it's true. But I've seen a lot of kids who certainly could grasp and handle the intellectual aspects of school, but emotionally still needed to grow a bit. It's OK to value your kid's emotional life as much as their intellectual growth.]
3. Oh, I don't want to have to pay for another year of daycare/preschool! [My response - well, I am an at-home parent, so that's not an issue for us. I sympathize with you about how much that costs, though!]
Basically, I try to make it "all about our family" and our own decision and completely independent of the decisions the other person has made. That has been more difficult with my sister, since her dd's almost a year younger than dd1, and since she's chosen the opposite approach (push into school rather than enjoy another year off, and public school vs. our at-home schooling).
So far, quite a few people have been supportive -- Oh, that's wonderful that you get another year with her! I got an extra year with one of mine, also a fall baby, and it was so nice to have -- those sorts of responses.
Very few have been judgmental about it (it probably helped that we were on the other side of the cut-off).