This is the way I look at it - I've had pets that I loved dearly that have passed.... one in particular that really got my heart....
When they pass the grief can shut parts of your heart off if you let it , it's so painful - who would WANT to feel that?
One pet I had taught me that even though the pain of losing her was so sad I was blessed every moment that she was with me.
I'd go through that sorrow all over to have more time with her. She lived her life with such joy and she never fussed or complained, 
never said no to a hug, never  gave me the imprssion that she'd rather do anything else than BE WITH ME.  
Even on the most mundane of days - she'd keep me company when I cooked dinner , or rest her head on my lap when I watched TV
or be the first one to greet me when I got home.   There wasn't anything that she couldn't "make better" and she couldn't even TALK!!!  
She taught me to open up my heart and share love with another pet who needed a home. 
Even fresh with the knowledge that the new pet may pass one day too - but I can be THERE for them
just like my pet was for me.  This new pet would never go a day not knowing they are loved too and that is EVERYTHING. 
Some people go their whole life never knowing they are loved by anyone not even another person, that's not what we are on this earth for,
if we were we'd be all alone - look around ...... people and animals everywhere !!! 
The new pet may not be  nything like the old pet which is fine.
Honour it's love and life and share.  Let it grow in the heart of another.
That once you have this kind of love you can't turn it off. It will make your own heart stronger.    
If you aren't able to adopt this beauty or a pup - keep looking - you are looking NOW because you KNOW something is missing....
(BTW : my pet was a 5yr old pet shop cat who passed 16+ years ago and I still think about her.
I have lots of love around me people and pets but if she hadn't have left that mark on my heart I may not have
realized how blessed I was/I am)