I'm 40 and am as sure as I can be without an official diagnosis that I have Aspergers/HFA. Childhood was not easy and it got worse. I wished I had known the reason why I was different. Eventually at 13 I refused to go to school, I was supposed to see the ed psych but I ran away the morning of the appointment because the thought of sitting in a room and being expected to speak to a complete stranger terrified me. What I did, to avoid anyone noticing me was to internalise it all. I ended up depressed, self-harming and bulimic then used alcohol when I was old enough. I couldn't ever understand why I couldn't be social, make small talk and just get through life like everyone else seemed to.
ds2 was diagnosed just before he was 3 last year and so I did buckets of research and saw myself described and every issue I had fit, selective mutism when little, tics and twitches, obsessions, routines, repetition. I didn't even know I used echolalia. It was such a massive relief initially, that there was a reason, that I wasn't just shit at being a human being. But then I crashed because it changed my whole history, it explained the times things went horribly wrong with people and that I must have come across as so strange and messed up to them.
Anyway, I also realised ds1 most likely is as well and last year when he was having another why am I so weird bout of misery I told him he most likely was. He's bloomed since then though we're waiting to see how he deals with secondary to see if we need a diagnosis.
I would say, with the problems your dd already has that I would definitely go for a diagnosis. It helps with getting help in new educational environments and it will help her understand herself. That's not to say she wouldn't take it badly initially, but in my experience, it would be better in the long run.