Every kid is different, but I will tell you what my experience has been: My now four-year-old has been dressing herself independently for about eight or nine months now. She still needs help with tights and weird stuff like that. She needs demonstrations on new stuff, like the first time she encountered a buckle, for example.
I don't remember when my 11-year-old started dressing herself, and that tells me one thing - that it must not have been traumatic and it must've come in due time.
One thing that really has helped my four-year-old with the concept of getting dressed independently (and helped my 11-year-old too) is a giant chest chock full of dress-up clothes. Clearly, I'm not going to sit by her for the two solid hours she sometimes plays with the dress-up bin (as we call it). So, consequently, she HAS to put the princess costume, bride costume, owl costume, ect. on herself. She may wander in while I'm doing what I'm doing and ask for a button-up in the back or to fix a difficult zipper, but for the most part, she'll dress and undress for hours on end. Great practice, eh? And she's PLAYING!
I believe between three and a half and four and a half is probably a pretty "normal" time frame to expect your daughter to have the motor skills to button, zip, etc. and to dress herself without your help But...as I said before, every kid is different.