Hi G.,
When I was a nanny, it was often the case that kids *hated* having to do all of those tasks in order to leave the house to go to....well, just about anywhere. One of the kids I cared for did half-day (afternoon) kindergarten and still had a lot of digging in her heels going on during that 'time to get ready' transition.
First, just know that your kid IS in a sort of 'habit' of being upset about this. I would back off from giving too much discussion and just give a short empathetic response "yep, you'd like to stay home and play".... and keep the morning moving.
Some things which made life easier:
Keep the TV off in the mornings. I can't tell you how much this can derail a kid's attention. NO tv time until after school. They will not die.
Schedule 10 minutes of bathroom time as 'together' time in the morning. Get your girl a sensible haircut (I endured hearing years of screaming as a nanny.... I feel your pain) that doesn't need much other than a brush. A cute bob works on nearly every kid. Also, brush their hair at bedtime the night before because it will work out any of that day's tangles.
Brush her teeth with her, while you sing a song or tell a joke, just get it done.
Have getting dressed take place before breakfast. Want food? Get dressed. Lay clothes out the night before. Some kids might choose to sleep in what they would wear to school the next day. Unconventional, but it solves a lot of problems if your kid isn't a sweaty sleeper. Even if it's tomorrow's t shirt and a pair of pj pants... if everything else is ready to, so much the better.
Every day she does well, no complaining, makes an effort-- heap on the praise. Be specific: thanks for coming to the table all dressed; you were so helpful in holding still while we got your hair brushed....
Remember, that the morning transition is all about her separating from you and doing something she might partly enjoy but feel conflicted over. So, there's bound to be some reticence on her part. Whenever you can, give her lots of personal positive physical touch-- a squeeze on her shoulder, a kiss on her head-- a lot of these can help because they give her the powerful, nonverbal message that you see her, value her, love her, just for who she is.
If you need to, consider waking 20 minutes earlier; you might need an earlier bedtime if the kids are dragging. It IS a long day, so be sure she's getting the opportunity to sleep at least 10 hours or so.
Hang in there!