"Do you have your own doll?"
Translation:Ĉu vi havas propran pupon?
I'm still learning but here's what I've found about the reflexive pronoun rule:
The reflexive pronoun "si" is used with the third person (he/him, she/her, they, them) not for the second person or first person.
Do you have your doll? - Ĉu vi havas vian pupon?
Do you have your own doll? - Ĉu vi havas propran pupon?