Yes get another pet immediately, as soon as you can find the right one. It is amazing how much it soothes your grief. I had to wait about 5 weeks until the pup was 8 weeks old so she could be shipped to me but I got a full sister to the 1 1/2 year old that had died. Some of us get so attached that we become despondent and getting another one soon is the answer not suicide but there may have been other things going on with this couple.
Don't you think you should go thru the entire greiving process first? Getting another pet right away is a mental crutch to avoid mental pain and suffering.
I didn't have pets growning up, and after my very 1st dog died(when I was 34 and I hadn't had a child yet), I'm SO glad I waited a couple months to get another dog.