We usually say "Đứa trẻ ăn khỏe, (và) ngủ khỏe" and you also say shorter "Đứa trẻ ăn ngủ khỏe. They are same. "Và" (and) rarely uses in talking it uses more in writting.
So funny. Ăn ngủ means eating and sleeping. Be careful when you use "ăn nằm" because it means make love with someone.