I am so, so sorry! Having survived four cats, I really know how you feel. One was with us for 18 years - same time most children stay at home, the others 11, 12 and 14 yrs. Grief can be overwhelming, but you will come out the other side eventually.
We have a new kitty - he found us! last January. Just walked in the patio door one day with his tail high and his nose twitching, and he has been here ever since. A gift from the Almighty. When hubby took him to have him neutered, vet said he was about a year old. Despite his unique personality, some of his antics remind us of the others, and we tell him how he is like one of his "brothers."
I'm glad you have a new canine friend. Love him 'real hard' ... he'll listen when you tell him about his older predecessor. Talking about your grief helps get you through.