I'm so sorry for your loss.
People that don't own pets won't understand what it's like.. They'll say 'it's just a dog, get another' but not realize it's not that simple. I lost my first dog when he was not quite 12 years old; it was a real nice day in June, sunny in the morning, not too hot. Storm rolled in in the afternoon. My dog was so scared of thunder, so we had to get him inside. He shut down on the porch, stumbled into the house, staggered through the kitchen into the living room and laid down in front of the front door, where he often slept. He just.. died. No warning. He was fine in the morning and in the afternoon, he was gone.. and it hurt like hell. It hurt. Like. Hell. I'm pretty sure that was the only time I saw my dad cry. Dogs are much better people than actual people are. Some people will never understand.
I did get another dog and I love my boy to bits and pieces. He's had all kinds of problems but I love him to death anyway; he's as close to a child as I'll ever have. I know he's not going to live forever but just the thought of it is hard to bear.
Go through the process. It's normal to grieve for a dog. They are family, too.