peakaboo, agree that the anticipation is worse than the reality. But then you get into the swing of things. It WILL be the most stressful time of your day. I do feel I have climbed Mt Everest by the time I sink gratefully into the comfy chair at work and switch on my pc.
dh and I used to wake at 6 am and were out of the house (dh at 7 am, me at 7:30am) with both dcs 4 and 1, dressed for nursery and in school uniform and we have only one bathroom in our house. Then we got an aupair and she got ds dressed so that I could leave the house with dd earlier.
The mornings were run on a military schedule, especially re: the use of the bathroom.
On your dd waking at 4 am, is there any way you can put her to bed later? Ideally, she should wake after you and dh so that both of you get dressed before she does. I shower in the evening to save time. Dh showers in the morning because he is smellier.
Dh gets up first because he takes longer to get ready. Then I wake 10 minutes later. We just have a cup of tea at home but breakfast in the office. Definitely use your nursery for breakfast. You can give your dd a cracker to munch in the meantime if she is hungry.
If the baby wakes during this time, we take turns to hold him whilst the other rushes their routine. We build 15 minutes' grace into the routine.