Small change of plans (for the better, yay!): It should be fine if you stay here the night. Inquired again, explained, etc, and they said it's okay. Pretty sure we have a spare mattress or inflatable one somewhere if you don't mind those.
I'll have to think of stuff to do in Melbourne. We have a nice aquarium (my default suggestion for people holidaying in Melbourne ) if that tickles your fancy! :3