As we've said its not only a case of finding students who want to share with a dog, its finding students who also don't really care about where they live - you will have very few options available to you meaning you will have to take whatever accommodation you and your dog can get, and people are generally fussy and have certain requirements (such as living in the centre etc). We're not saying that no one is going to want to live with a dog, we're saying it will be difficult to find somewhere to live with a dog in Edinburgh.
But as Michaela said, do what you want - it's your decision at the end of the day. But you asked for advice and we're giving it to you based on what we know having lived, rented and owned flats in Edinburgh over the last 3 years or so. What you do with that is up to you and in all likelihood you will probably find a way to bring your dog if you really want to, but at what cost (financial and otherwise) and what comprimise that is to you, that is another matter entirely.