Fermentation will be done well before three weeks. And it's something you can monitor as well, so if all the gunk has risen out of the beer and it's stopped bubbling much, (probably a week to 10 days at most) it's fermented and there really isn't any reason not to move it to bottles.
And while it's not going to be 'ready' for some time, there really isn't any harm in tasting it along the way. Gives you appreciation for the process. If you have any of those..I'm drawing a blank on the name of them, the cork pop-top style bottles that reseal, can probably cheat and pour out an ounce or two out of that for tasting every week or so.
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