Are questions about pet loss, grief, etc on topic for this site, or are they better suited for Cognitive Sciences?
Questions asking how to help owner's cope with any kind of emotional issue due to their pet is off topic, it's not about the pet, it's about the owner's welfare. It's not a grief and loss site, it's a site concerning the welfare of our pets.
This is a good example of what's on topic, helping a pet cope with the loss of another pet.
I can see that as being on-topic, but unless the question is a little bit more detailed and specific, I'd wait until after we've been in public beta before asking questions like this.
We should remember that the goal of the private beta is to maximize the chances of attracting experts to the site who will be able to answer the really tough questions. If there are too many basic "list things for me" type questions where the questions appear to be asked by what could be construed as amateurs, then it may not attract experts. Basically, all of us that are here for the private beta are tasked with designing an expert level Q&A site.
Most people who have cared for a pet should broadly know techniques for how to cope with the loss of a pet, so such a question tends to be more of a "getting to know you" type question. See Good Subjective, Bad Subjective for more details. Also, such questions don't require the same level of expertise as a real, actual problem.
With that said, I'm not saying the question is a bad question, and it actually got one really good answer. There's a lot of different directions we can take this question in terms of editing in order to get it reopened and reopen it as a stellar example of an expert level Pets Stack Exchange question. The best questions, the ones we should ask in the private beta, are about real, actual problems we're facing, and I support editing the question to add more details and depth, or rewording it so it has a real actual backstory (or a perceived, made-up backstory that paints a stronger picture of a real, actual pet loss):
I lost my dog this week due to an illness. He was very young and this was a surprise. The vet said he died due to X disease, which should have been preventable if I hadn't missed one of his vaccinations. I didn't mean to miss it, but I'm working 60 hours per week to save money for school and lost track of time. I don't have kids and have never really lost anyone close to me, and this was my first pet.
I feel sick to my stomach all the time, am wracked with guilt, and feel responsible. What techniques can I use to cope with the loss of my dog?
I know my version is very macabre and depressing, perhaps even evoking some strong emotions in people who feel there's no excuse for negligence, but I hope this helps inspire what's possible with this question to paint a more detailed, interesting picture that will attract people with deep experience in this subject. Hope this helps!