just a guess that you will get between about a quart a day. We don't have miniature but have large size goats. It will vary according to hold long it has been since they had babies.
Preparation, cleaning, etc of the goat - About 15 minutes per goat for us on large goats
Hand milking each large goat depends on again, how long since baby and how much this goat will milk in general. We have one nubian who still produces almost a gallon a day and another nubian only 1/2 gallon a day.
After milking you will strain and refrigerate milk. Depends on your speed but I would say at least 45 minutes to 1 hour 15..... And we milk twice a day not once, twice is better for the goats health but that would depend on your schedule.... Good luck!
It varies a bit depending on their breeding but we have two in milk right now and get about 4 liters per day, milking about 12 hours apart. In total, the routine takes me about 25 minutes (get grain, wash and dry udders, milk, cover, then switch does and repeat). You might find a wider range of info on the on BYC's sister site, BackYardHerds.com if you have more goat questions.
The speed of hand milking, from the time you sit down to milk until she is finished, depends on you. It is tiresome work until you build the muscles for it and don't be disheartened if it seems incredibly slow at first. Speed and stamina will come with experience. My milking experience lies with cattle, so I can't say anything about the milk production of a Nigerian Dwarf. Have fun with your goats!