Yes, that works.
From the Comprehensive Rules:
122.1d A stun counter on a permanent creates a replacement effect that stops the permanent from untapping. That effect is “If a permanent with a stun counter on it would become untapped, instead remove a stun counter from it.”
What's notable here is what it doesn't say. Stun counters prevent a creature from untapping. They don't prevent it from doing anything else that it would normally have to tap to do, if you can find a way to do that thing that doesn't require tapping it. Doors of Durin is just such a way.
A vaguely related rules interaction: I had a game recently where I was able to attack [[The Eternal Wanderer]] with two creatures (despite its static ability that disallows that) because one of them was a token from [[Adeline]].
