Your sentence is very clear and mostly correct! Here is a slightly improved version for better grammar and flow:
"The penguin dad gently holds the egg on his feet and covers it with his soft feathers. While the dad keeps the egg warm, the mother swims far into the ocean to catch fish for her family."
Explanation: We change "hold" to "holds" because the subject "penguin dad" is singular, so the verb should have an 's' in the present tense.
Everything else in the sentence is perfect and easy to understand for a 7-year-old!