Fish and Eggs take about 1 minute, and Other Meats take about 3 minutes!
Complex foods vary in the amount of time they take to cook. Pumpkin Pie takes 10 minutes, and Bug Soup takes 7, I think?
Then combine this information with the level increase giving cooking speed, and you'll be able to determine approximate time a bit better, with the aid of a calculator.
The bears in caves drop eggs, along with many other enemies, but you'll have a higher chance to burn eggs until you reach a certain level in cooking.
However, I'd actually recommend gathering Fish! Most fish can be cooked from level 1, besides the Koi.
You can get fish by using the Fishing profession, and then gathering additional fish via grinding the area in Darkspine called “The Neck”. The Grimalkins there Drop a LOT of fish, presumably because they're cats. They also have a high chance of dropping plushie trinkets that can be sold for a lot of pebbles via the “sell to vendor” option in your inventory, and Blue Agates that can be sold on the flea market for a moonstone or two.