Why don't you need a classifier here? I thought if it is a "specific" bed you'd use the classifier. "It" would suggest to me it is a "specific" bed and not "beds" in general?
Sometimes when there is a possessive like "của chúng tôi" the classifier can be omitted. Which is kind of a vague rule, but at the moment my knowledge stops here, sorry.
another way is "do la" still don't get y they would use "no la"
Different dialect maybe? I've heard both and both are widely understood.
Nó is it, dó is that.
Nó là cái giường của chúng tôi.