Sounds okay to me. The main things to cover are LOOK, GET, DROP, INVENTORY and one or two other commands such as LOCK, UNLOCK, OPEN & CLOSE. Also, don't forget movement.
In your case, after getting the key, tell them about INVENTORY (or I) to see what they're carrying. After unlocking the door, you can tell them how to DROP KEY, as it's no longer needed. After opening the door, you can tell them about movement (N, S, E, W, U, D).