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.