No, get another dog right away, it heals the hurt. I am speaking from experience, I have owned and lost dozens of dogs. A dearly beloved dog can be replaced, the old one won't be forgotten (I still miss Tootie) but you have the new one (Cookie) to love and focus your attention on. I have lost a child too and there is no comparison in the experiences. A child can't be replaced and you must spend time grieving. People who try to put it behind them with drugs and alcohol or another relationship are using a crutch and they are just fooling themselves.
I believe you have explained this in your opening sentence "I have owned and lost dozens of dogs". I REALLY think you need to wait after the 1st one goes. Subsequent ones can be replaced easier.
SOME people treat their dogs like a child instead of a pet. For THOSE people, waiting is very important.
You seem to have a pretty well balanced nature about such things(given your horrible experience). Getting another dog right away works for you because of it. But for those who anthropomorphize their pets, they need more time. This couple is a perfect example.
I know you'd never do this over the loss of a pet, but for those who think about taking such drastic actions, they need to grieve properly.