Personally, I feel that "a soul is a soul is a soul...." It doesn't matter whether that soul was a human, animal or any other kind of soul.....
Firstly, though, let me offer my condolences on the loss of your lovers canary.... Sometimes it is the more subtle things which can hit us the hardest.... But try and look at it this way - the canary has gone "home", back to where he or she came from.
I recently had to put my 25 year old cat to sleep, this past Dec., just before x-mas. I have known his soul much longer than I have known many people. So I can honestly say to you that yes, animal's souls are just as important as people's souls (and sometimes more pure). And I have felt his presence since his passing.... It's difficult to describe, I can just feel him around, sometimes. But then, he had kept me company through slightly more than two thirds of my life.... (I am 36, I had him as a companion since I was 11 years old..)
I have also buried quite a few cats, my own as well as strays that got run over here in New Orleans. I always try to take some sort of personal responsibility for the souls of the strays, for they never had anyone to care about them, at all. I just try to remember them and hope that "home" is kind to them, granting them access unto the "eternal purr", or at the very least a trip back here into a good home, or a well stocked hunting ground ;)
Sometimes the hardest thing about Death is to realize that we will never again know the touch, sight, sound, smell or feel of that which has passed. And at times it is this which is what makes us grieve. But, if you reflect upon that soul's freedom from the physical form, if even for a brief time until it reincarnates (or not).... well, there is something in that which may or may not make the grieving less harsh ;)
If a soul has enriched your life, you will remember them always, and if you have touched others, they will remember you always.... This is part of how things continue.....
"And one by one we died and were lost in the dust of accumulated time. We knew the years as a passing of shadows, and death itself as the yeilding of twilight unto night." - Clark Ashton Smith