Any small animal vet will offer cremation services.  However, it may be expensive.  
Based on illness, I am not sure that I would want to put into a freezer that you use for food.  I believe viruses can survive being frozen; medical researchers have recently recovered some of the 1918 flu virus from frozen bodies of people that died of it.  I happened to look this up recently because I was very ill after insulating my tenant's attic, and I had pulled out some old newspaper clippings and a medicine bottle from early 1919, while the 1918 flu was still running through the U.S.  So I wanted to know under what conditions that virus could survive.  Frozen, yes.  Attic conditions, no.  
So I would think it is better to burn vs. freeze.  And not compost.