I don't feel that losing one dog is any reason to get another dog. If Gonzo or Fozzie died... it would take months for me to get over that. I think my heart would be so broken if Fozzie died, especially, as he's my little ray of sunshine. If I got another dog soon after I know all I would be doing was comparing that dog to Fozzie. And nobody compares to him.
Once I was done grieving the loss, I'd take time to figure out what I want in my next dog and what breeder/venue I want to go through. Then I'd find the perfect breeder and wait for the perfect litter, or wait for the perfect rescue dog to show up. I would not run out the next day and desperately look for a dog to "replace" my other dog. Dogs are individuals and one cannot replace the other. I do find it unhealthy when people start looking for a new dog right away, especially if their old dog got lost or was taken from them. I would hope that they'd at least take a while to think about that loss, and really dedicate themselves to getting educated & improving whatever caused them to lose their dog. And to do their research and find a breed/dog that they will keep for life! I know a girl who started looking for GSD breeders a week after her dog got lost, while still looking for him... and he was found at a shelter, but she didn't even get him back. He was only 8 months old. Ugh disgusting.
When ever my dogs have died, we've always had at least one other dog, so we were in no rush to get another dog. I feel like it's insulting to that dog to instantly replace them. And I get dogs because I really want that dog and for no other reason, I have to pine for & obsess over a specific breed for YEARS before I'll even consider committing to buying one. I wanted a Border Collie for most of my life before I got Gonzo. I wanted a Corgi for 5 years before I got Fozzie. It's a big deal and I never want to be disappointed or end up re-homing a dog because I didn't do my research or changed my mind.