I'm a "be on time if not early" person, so I feel for you.
I realize that at 4 your DD more than likely has toys all over her room, but with my daughter we kept them in the closet so as not to distract her, and set her clothes out the night before where she would see them in the morning. We had it worked out to a science as far as timing. There was a TV show she liked to watch, so that was her incentive to get up, shower, (she was like me and preferred to bathe in the morning) dress completely, then watch her TV show as she ate her breakfast. I did her hair as she watched the show as well. When the show ended she went to brush her teeth, and use the bathroom, jackets were hung by the door so all she had to do was grab her lunch pail from the counter and her jacket and we were out the door. There was no need to fuss at her, she knew that to watch her show and get out the door to get to her preschool this is what she had to do. She did this from the time she was 3 and 3 months, until she was in 6th grade, I'd just stopped doing her hair ; )
Do you have an incentive that would motivate your daughter to do what she needs to do? A TV show, DVD, or a video game she wants to play? Say, if she gets ready without you needing to remind her she gets to watch it for 30 minutes in the afternoon or evening. Or have you tried making getting ready a game? Wake her up and say something like, "First one dressed with shoes on gets to pick the radio station (or CD) for the drive to school." Then the two of you race to get dressed, and if she beats you she gets to pick. Or she gets to pick her treat in her lunch, etc.
Another option I am sure will label me as "harsh" is to have her miss out on something if she isn't ready by a certain time. I think what opened my daughter's eyes when she was still in preschool was when I told her our friend and her son (my daughter's best friend) were on their way to pick her up for breakfast and the park one Saturday morning. She had about 25 minutes to dress (I didn't care if she showered, and I put an outfit of jeans, top, sweatshirt, and socks on her bed.) She wouldn't get up from watching TV, and when the doorbell rang she jumped up, ran to answer the door, and she and her friend proceeded to watch TV. I said something like, "Get dressed so you can go eat and go to the park" and she didn't make a move. I set a timer for 5 minutes, and it went off without her budging. I told my friend that she wasn't going to go after all, and she jumped up and ran to her room, but it was too late. My friend and her son left, my daughter begged me to take her to the restaurant they were having breakfast at, I stood my ground and refused, and as time wore on she asked me to drop her off at the park and I refused. But she learned her lesson at 4, when Mom tells you to do something you better do it. Another way would be if your DD took too long and the two of you wouldn't be able to do something special like stop for ice cream or yogurt, not enough time.
And, a timer is invaluable. If you set it for the amount of time she needs to dress, then eat, brush her teeth, etc., it gives her something to gauge herself by, and there's no need to fuss or remind. She'll see that taking her time makes her run out of time and that she needs to speed up.
Encourage her when she does well so she isn't just hearing what she perceives as negative, with kids who seek approval big-time you have to walk a fine line. As far as your patience, do a task that keeps you busy so you're not dwelling on her dawdling, and hang in there.