My wife is kind of the fermented food expert in our house, although I get in on the process too. She just does all the reading. She tells me that any ferment with cabbage really should go for 10-12 weeks for complete fermentation.
You'll probably get some sour flavor development after a couple weeks though. It will stay salty for quite a while and then start evolving. Be ready to punch it down and vent the gases often in such a small container.
We've since moved to 1-gallon bail-top glass jars that I think we ordered from Harbor Freight. We had the lids drilled at a glass shop to fit the #9 stoppers which accept an airlock. Since we managed to finally exclude oxygen from the fermentations, the results have been much cleaner and better tasting. We monkeyed around with quart and 2-quart jars for quite a while and never could quite get them to seal completely.
Either way, this should be a fun project for you. Good luck!