There is one thing I'd look for when thinking this through: do you think there's anything else going on that might be causing anxiety for your dd that's somewhat under the surface of the obvious?
Two of my children had what seemed like irrational fears when they were your dd's age - and those fears turned out to be due to something else entirely unrelated to what they seemed to be related to. 2e ds worried terribly about people breaking into our house, and the worries got so bad he started being afraid of going outside to play in our yard. What was really going on was stress at school due to an undiagnosed 2nd e - but he was too young to understand what was so stressful about school, and his stress came out in what seemed like irrational anxiety. Once he had a diagnosis and help with is 2nd e, the fear of robbers and the outdoors disappeared almost overnight.
One of my dds was beyond scared of going into the movie theater or public places crowded with lots of people. She'd get so stressed she'd cry so and just couldn't go in. We found out at the end of 2nd grade she had severe double vision (we'd had no clue earlier - she never said anything about troubles with seeing two of everything). Her severe anxiety over going into a movie theater or crowded public place disappeared once her vision had been corrected. OTOH, she's still crazy scared of heights... which I suspect may be due to her vision (she still has very limited peripheral vision). And she's now insanely scared of spiders. So much so she's basically infamous for it at school. She's never been bitten by a spider and the spiders in our part of the world are truly very small - I can't think of any logical reason she would be scared of them - but scared out of her mind crazy by spiders, that's my dd. Totally irrational. Don't think it's an indication of anything else other than thinking spiders are freaky scary looking. Not to worry you, but my dd has now been crazy-scared of spiders for years... I've tried quite a few things to help her get over it... and I think now it's just her "something" that isn't going away.
Which leads into the second thing I'll suggest thinking through: does your dd tend to have an anxious personality, or is she only anxious in these situations? Some people are just anxious by nature. My ds, for example, doesn't walk around constantly anxious but he reacts to stress with anxiety. So for the most part, as long as his world isn't filled with unnecessary stress, his anxiety isn't something that is such a huge issue he needs help with it - he just needs help sometimes dealing with stress in specific situations, and we can manage helping with that as parents.
My younger dd, however, has an extremely anxious personality. She's never had what seem to be irrational fears, but she has a ton of worries. We've worked through the book KJP mentions and it was really helpful. She also saw a counselor for her anxiety briefly when she was younger (around 7) and that didn't work out to well. It helped a little, but didn't help long-term. Maturing hasn't helped the worries really go away, but it has helped dd learn how to manage them much better.
And... the last thing I'll add... my dd with the vision issue - correcting the vision issue took care of the irrational fears - *the ones we could see*. She seems to be an incredibly happy-go-lucky kid on the outside who is always laughing, smiling, cheering everybody else up and onward. I didn't find out until she was a teen that deep down inside, she still had a lot of worries that she wasn't sharing with anyone. So, fwiw, there's something positive to be said for anxiety and irrational fears that you can *see* and know your child is experiencing. Those obvious and irrational fears may go away, but keep talking with your dd and try to keep in touch with what she's feeling as best you can.
Best wishes,
polarbear
