Stripping the current laws back to their basics, you can’t ban pets unreasonably which means, literally, without good reason.
That means you can’t ban dogs because they might bark all day and night. However, you can get rid of them if they do.
There’s a widely ignored section of the law that deals with animals that have been allowed but later prove to be a nuisance, so there are mechanisms available to remove problem animals, however that tends to reinforce the argument against unreasonable bans.
As for tricky laws to limit the size of dogs, there was a recent case (albeit in Queensland) where a dog owner successfully fought a by-law that required them to carry their dog in common property or walk it up 15 flights of fire stairs, because that effectively prevented them from keeping their dog.
All of which is to say, if you can’t identify a specific issue – such as a resident having a genuine phobia of dogs or a life-threatening allergy – you could be on a sticky wicket.
The size of the dog would be an issue if you had particularly small lift or passageways, so that people wouldn’t be able to avoid close contact.
But I think your best bet is to make the resident aware that if the dog proves to be a nuisance, you have options to have it removed from the building.
If appropriate, you might also give permission on condition that it be muzzled when on common property and that the owner doesn’t take it into the lift if there is someone already in it.