I think it's a perfectly good idea to get another quickly - and it it no way means you're 'over it'. Probably the only reason it's not a good idea with any human companion you might lose is that the new one will tend to understand the situation and possibly not cope well/get hung up on it (not happened to me, but it could). You never 'get over' a bereavement like that of a human or a much loved pet like a cat or dog. You eventually come to terms with it, and at the time, maybe, you just have to 'get on' with it.
Keep looking Snapper, the right dog is out there, and you'll find them, it's just a question of letting fate do the introduction.
There was an interesting thing on the radio a few weeks back, about how people aren't allowed to adopt a child to 'replace' one who dies (although it isn't like that, really, and the potential adopter may be a fantastic parent), until quite a long time after - a couple of years. Of course, there's nothing to stop someone who can, just getting pregnant whenever they like. But I digress...