I believe the answer you are looking for is free range. No one likes a whale in a cage!
Whales often visit the same areas every year. You can have a harvesting bonanza once a year and stock up your food reserves. Think this sounds implausible? We only have one harvest of grain a year, sugar takes two years. We bring it in all at once, and store it for the rest of the year.
Various regions harvest at different times, and sell any excess to their neighbours. So you can have cross country distribution of your whale meat providing all year coverage. You will have to harvest alot, and find a way to preserve the meat without it going rancid. Whale biltong just does not sound right!
Australia cattle farming is a good example of what I'm talking about. The cattle are fully domesticated but have huge huge ranges. Farms are so big, the farmers have to use helicopters to quickly find where the cattle are. It used to take weeks to bring the cattle in on horseback. Now I think it takes a few days to a week on quad bikes.
You will probably need to try keep the meat as fresh as long as possible. The entire planet doesn't have a handy freezer like the Eskimos.(sorry if that word offends anyone). You will need a vast network of whale hunting and harvesting boats and ships. Technology level up to you. You will track your whales and maybe keep constant tabs on them to reduce finding times when you get hungry. Whale shepherds!
You then know how many whales you can take in each harvest and still keep a healthy genetic pool. Harvest any whales that refuse to breed!
Ensure that any sea captains that have a grudge against any white whales are only allowed to captain a ship when said white whale is not pregnant or nursing.
Along the same lines, alot of the beef meat we eat are from the males (sorry guys). You only need a few stud bulls to fertilise the breeding females, dairy cows (maybe you could investigate utilising the whalecows milk. I think you will have to invest in some scuba gear). Maybe your genetic engineers can tinker with a couple of genes and make it obvious from a surface viewers point of view if they are about to harpoon a male or female. I'm thinking skin colour or something 'small' like that.
While you are busy genetically modifying the whales. If you track the whales you will figure out which ones are breeding faster and more often. Kill off the slow and lazy ones. Allow 'survival of the fittest' to take its course.
If you can keep tabs on the whales, co-ordinate all along the coastline and with your vast mobile armada of whale hunters (sorry, caring whale shepherds),you won't necessarily have to 'domesticate' and 'tame' the whales. Ostrich are farmed for both their feathers and meat and they are certainly not considered domesticated.
EDIT considering you new world only has plankton, krill and whales...No predators. You can remove the young from their mothers a few months (maybe 6months) after they are no longer dependant on mother's milk. No need to protect a youngster for 2-3 years if there is nothing to protect against.
You may have to move the young to some aquariums completely removed from the ocean so that they don't communicate with mother dear. Let mother grieve for awhile and a few months later to a year she could possibly be pregnant again. This will increase productivity!
The youngsters meanwhile are being handled and dependant of humans and will become 'friendly' and not perceive us as a threat (suckers). Once these youngsters are brainwashed they can be released back into the wild to feed themselves.
A few years later...yummy steak on your table.
I sometimes wonder about the way worldbuilding brings out the absolute evil in us all!