From my point of view, it's not really about believing, it's about explaning death to them. Easier to have them think it'll all be ok, than wake up in the night crying.
Your child is very young and it is difficult to explain death to them. My grandmother died when I was 12, and my mother told me Granny was watching me all the time and was with me. I didn't know Granny very well, but she was terrifying and the thought of her watching everything I did was very disconcerting and upsetting. My own children had pets, fish and hamsters which didn't live very long. Though they were heartbroken when the pets died, they learnt to appreciate that not everyone and everything lasts for ever. When their young cousin died, it was very hard for them to take, and it was easier to say their cousin was with the angels and had become one.