Agree with all thas has been said. When we grieve for a human relative, that grief is at least socially recognized. You are given some time and more important your loss is acknowledge through formal means. Funerals aren't for everyone but they do serve a useful social function. With pets, the grief feels more personal because it seems like there's no collective recognition that this life had meaning and importance. At least you'll find that all the people who have been through it too are very supportive and understanding.
I had a similar situation a few years back with the original King Kat. He and his sister were my first adult pets (first pets period actually, my parents hate domestic animals). He was just the gentlest most affectionate creature and I really wanted him to stay with me forever and I don't think I'll ever build such a strong bond with another cat. I'd say it probably took me a full year to trully and fully grieve. I don't doubt that you did everything you could possibly do for your dog.