My son started tae kwon do at 3...and he is now 5 almost 6...we moved to a new studio and changed to Mu Sool Won (still Korean martial arts, but more fluid and less "choppy" and I think better on his joints, etc). They stress learning to fall and pressure point and joint holds. Along with the forms they learn.
We found an awesome instructor, who understands child development and doesn't expect un-age appropriate behavior...he gets the kids are young.
My son just received his green belt and the youngest in his class, I think it annoys the 9 and 11 year olds that he out ranks them...but he has been doing it longer. My daughter will start at 4...that is the youngest this studio will take her. She can't wait.
My husband's has always said our kids would be in a martial art until they reached black belt and/or leave for college. He left it up to me which one. he wants them to be able to protect themselves and feel confident.
Let her try it and see if she likes it...you get a least one free class...and usually can get a short like 6 week trial contract to see if she continues to like it. Be wary of long term contracts...some of them just want your money and don't really care about your child...and other places will advance your child whether they are ready or not, just to get the testing fees (which can be expensive), and so you have to buy new belts and patches.
If you have a friend who works at the dojo then I think that is a great place to start...and join her and take too...I hope to start taking classes one day...my son might be my instructor. ;-)