I myself made a dough fermenting tub out of a small plastic tub and drilled a 3/8 inch hole in the lid. Then I installed a rubber grommet into the hole and the attached a fermenting airlock in the grommet to release the gases and not allowing any air to get into the tub. These air locks can be purchased at any home brew shop or on line at websites like www.beer-wine.com/ do note the size diameter hole you need to drill will differ from the manufacture of the air lock. So purchase your air locks and grommets first then drill the hole in the cover.
Hmm, nice idea. I have been brewing beer for years. I have a drawer full of airlocks. One drawback that I can think of though is that the containers can't be stacked in the refrigerator.
Actually, now that I think of it, a tiny hole on top should work fine. Since CO2
is heavier than air, there will always be a layer of it on top of the dough that cannot be displaced by the lighter air in the refrigerator. This is why some homebrewers just put plastic wrap on top of their fermenters instead of a lid with an airlock. I usually only use an airlock for carboys.