Having a pet for 12 years is a long time of laughter, love and even tears. I just recently had to put down my Simba of 17+ years. Kidney failure. Happened unexpectedly and I was not ready at all for that. But, like you I loved him with all my heart and cried many many tears and on occasion still cry. But, the main thing is the memories we've had with them here on earth. The pain will pass and the beauty of having her in your lives will remain forever in your memory. I don't know about other people but I truly believe that they do go to heaven and I choose to believe that I will see them again some day.
You and your sweet baby will be in our prayers.