Isabelle Harris went into cardiac arrest at the Holmsley campsite in the New Forest early on Friday.
A police spokeswoman said poisoning from a barbecue was being looked into, but further test results were awaited.
Post-mortem tests showed the death was not suspicious.
Police are treating it as a “tragic incident”.
The girl’s parents have said they are “absolutely devastated” by her death.
Lee Harris, 30, and wife Tracey, 40, from Gosport, Hampshire said Isabelle was “a really special girl and this is a huge loss”.
Mr and Mrs Harris were arrested on suspicion of murder after the death but later released.