This is a tough one. My middle kid got some strange looks when she was about 11 - reading stuff meant for HS kids and people thought she was 8 years old. She just told people her age and then they started treating her like an 11 year old.
As for age cutoffs, my kids have just missed cutoffs for summer programs since they have late summer/early fall birthdays. If they wanted to be in the older group (since these were their school classmates), we just asked the program director. I don't think I ever had a problem. Many folks are understanding of the situation if you discuss it with them.
It may also help if someone can vouch for your kid. We did this when the older two entered HS and needed to skip some lower level foreign language courses. We had a teacher speak with the school admin and tell them the appropriate placement. If someone such as a teacher (or other adult, just not a parent) can discuss with the program director, it may help.
I think the small size hurt more in sports, and it continues to hurt middle kid. Folks naturally go for the bigger kids, and my skinny 16 year old (5'5", 105) doesn't look athletic, though she may be more capable than the bigger kids. It sometimes helps if someone with no preconceived notions about your kid judges her abilities. Definitely helped middle kid when she had a new coach in her fall sport - she ended up the only 10th grader on varsity. On the flip side, she has been around the spring sport coaches since she was in elementary school - and their preconceived notions of her ability persist.
My youngest is probably much like your DD - she is 9 (10 this summer) and she is 4'2", 46 lbs. Most folks think she is younger than 9. She speaks up for herself, much more so than middle kid, so I think this helps (if your DD is willing to speak up).
She has you to stand up for her now. Just wait until she is 25 and gets carded for the R rated movie (yes, this happened to me).