Well...we had a very different experience. DH and I took the twins 6 months ago, when they were a little over 2 years old. It was completely traumatic for us and for them. They both cried terribly through the whole experience. It was a pediatric dentist's office (although I've seen some since that looked like a lot more "fun") and the staff was nice. There were stuffed animals and murals of trains and fun things hanging from the ceilings. But my boys just do NOT like being in situations where they are made to sit still (haircuts, doctor appointments, photo sittings, their stroller, etc.) I think that's probably partly due to the fact that they were preemies and spent their first three months in the NICU.
The dentist tried to take x-rays. I have no idea if any of them turned out. The boys wouldn't stay sitting in the x-ray chair, so DH ended up sitting in the chair with one of those lead aprons on, with a screaming, struggling child on his lap (with his own apron on). It seemed like it took FOREVER (times two). I had to stand outside the door (to avoid radiation) which made it worse for the boys I'm sure. Then, for the check-up part of the visit, we again had to basically hold them down, straddled with their bottoms on DH's lap and their head on the dentist's lap while she took a quick look inside and swabbed them with something. The whole thing was just horrible.
I think the reason we decided to take them so young was because our insurance plan covers check-ups 100% and recommends taking them at 1yo, so we thought we were "behind". Also, a friend of ours had just taken her 3yo son and found out he had 5 cavities. So we wanted to make sure everything was OK. In hindsight, we feel like we didn't think it through very well and wish we had waited a year or more. Our boys were breastfed and we don't give them sugar, so the risk of them having cavities was really, really low. I'm concerned that the trauma far outweighed the benefit and I just hope we haven't set them up to hate the dentist forever.
Anyway...sounds like our experience wasn't the norm. If your DD does well at doctors appointments and haircuts, she'll probably do fine. But I also think you'd probably be OK to wait until she's a little older and can have things explained to her.