Hi Denise - I live just across the blue bridge from Owensboro, in Reo!
Not a strange question at all...and certainly one that is easier to think clearly about before it happens, rather than immediately after.
My Olivia died unexpectedly at the vet's office (in Owensboro!) when they gave her anesthetic for her dental.
They called me - but I thought they were calling me to pick her up...I was in total shock, crying and couldn't think straight. I told them I'd just have to call them back after I talked to my (grown) daughters. I like the other posters idea of having a little funeral when there are children in the home, I am sure that would help them understand better. But since I don't have any children at home, I decided to have her cremated and her ashes spread at the vet's farm...I like to picture my little Olivia running free with all the other doggies at the farm, chewing on toys - no longer hindered by the health problems that she had due to being neglected the first few years of her life. Silly, I know - but it gives me some comfort.