If there's a language rule that says you can't combine these two this way, I'd be more than happy to learn about it. English is not my mother language so I apologize for any grammar/spelling mistakes in advance ;-)
There's definitely no rule against it. I wouldn't think anything of hearing "who're" everyday conversation. It's rare you see it in writing, though.
What you hear in every day speech is governed more by the mechanics of how your mouth works when you're speaking fluently, honestly. For example, if I were to say, "I would have done it" it most likely would come out sounding like "I'd've done it." Unless your intention was to get the sound across, though, you'd never, ever write that.
However, for some reason, unlike more common contractions, it is much more common in spoken English than in written.
†http://dictionary.reference.com/browse/who're