Sometimes it seems like animals have more common sense then most people these days and they give love without ever expecting any in return. I know I'll probably feel heart-broken when the animals in my life "return home" one day.
The following is advice based on my past experiences with a "broken heart". I hope some of it is helpful.
Like Doug said, give yourself, and your other animal companions, time to grieve: cry your heart out, be depressed, worldly demands can wait.
There will be days when you wake up crying. And there will be days when you feel like life can begin again. I found it helpful to do something with the pain such as spending time in nature, writing a song/poem/whatever, helping someone else, getting back to a project that's been on-hold, or learning something new. In other words, keep the mind active even if it's just scribbling a picture on paper.
YOU WILL get through this even though you might be completely convinced otherwise at the moment. Believe it or not, one day you'll look back and think "man, that was a tough time in my life… but I survived."
Go be sad for awhile. You'll be OK, my friend.