I see that Rolling Acres has been recommended already. You can take the corpse to a Vet and they will dispose of it for a fee. You can always place the box that cat is currently in into another trash sack and just put it on the curb with the rest of your trash. Or you could dispose of the box in a nearby dumpster. Unless your grandmother's next cat is really old, in very poor health or extremely accident prone, I agree with you that it is very likely to outlive her. If you and your child are allergic to cats, please don't get another unless it won't contibute to your allergies. There are hairless cats, but they are somewhat expensive and kind of funny looking. Also, because they have no fur to protect them, you really should keep it indoors at all times. I'm very sorry for your and your grandmothers loss.