That's probably what most people do with their deceased pets. Some people might prefer (and be prepared to pay the expensive fees for) pet cemeteries, or to arrange for cremation (which is relatively inexpensive) but there's absolutely no reason why you can't bury a pet in your back garden.
In fact, it's generally perfectly legal to bury a deceased human in your back garden but it might cause a few problems when you try to sell the house!
I can only cocncur with Chris on this.
We have 4 cats buried in our garden(two bodily,and two sets of ashes).
We are lucky to have a large garden,but large or small it's OK.
Just remember WHERE you bury the pet,it could be traumatic to dig them up again!
Ours are under lawned areas,so we don't have to worry.
You should ensure that you make the grave deep enough or you may find that the body reappears overnight courtesy of various animals such as foxes, badgers etc. Also, if you want to mark the grave with a stone or similar, this can put off potential future owners.