Isn't it supposed to be 'COMING from home'?
Wouldn't 'coming' be 'venio'?
Grammatically speaking the correct question should be 'I'm coming from home' but according to the lesson's context the correct question should be 'I'm going home' : Ego domo eo.
"Going away" as in leaving would be more accurate. Some sort of explanation should be provided. Ablative case "domo" includes information that someone is moving away.