I used to have the same problem with my son, even if a dog was on lead he was scared to walk near it. I started to show him video clips on You Tube of dogs doing cute or funny thing, and although I wouldn't neccesarily recommend it, we did end up adopting a greyhound as we were both became particularly fond of them and they are such placid dogs. My son is no longer scare of any dogs.
As you are unable to have a dog yourself, I would suggest visiting greyhound rescue and introducing your daughter to the dogs, a lot of other rescue centres can be very noisy frightening places, whereas greyhounds are generally much quieter and calmer. If you explain to the staff your predicament, they should be able to select a dog who is particularly calm and good with kids and allow you to pet and even walk the dog as most are exceptionally good on lead.
Best of luck.