They answer in response to Bilbo's finding of the key by asking.... why on earth didn't you mention it before?!
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Durin's Day indicates that the dwarves can open the door with the key on the last moon of Autumn.
Bilbo's sharp eyes spot the tiny key. It had evidently fallen out of the pocket of one of the trolls. Otherwise, it would have been turned to stone like their clothes.
Mirth is happiness and joy. Shared laughter and smiles are key elements to mirth, along with song and dancing.
Stand by the grey stone when the thrush knocks, and the setting sun with the last light of Durin's Day will shine upon the key-hole
If you sang it a few times, or more than a few, it should stick. Your interest level would be the key.