"done eating" is correct and usable in written English.
You can use it when you want to refer to an event of having completed one's eating. For example, "I'm done eating - let's go for a walk."
STUDIO STOP When we're done eating, we'll head to Sarah's studio in Hell's Kitchen.
People who thought they were getting a low-calorie snack had hormone levels indicating that they weren't done eating.
It can take a while to get the waiter's attention and dishes can sit around long after you're done eating.
Mashed potatoes are Uncle Mike's favorite food; at family dinners he would spoon mound after mound of them onto his plate long after everyone else was done eating.
Also make sure you're done eating in 25 minutes.
He was done talking and done eating his burger.
The best pizza crusts are the ones you notice only after you're done eating.
I would wait until they are done eating and they go outside.
You don't have to load the dishwasher the minute everyone is done eating.
Another food aside: After you're done eating the oysters try the soft-shell crab.
One of them asked me to leave my seat at a dinner table because I was done eating.
