This doesn't comes under a valid contract.
No legal document is required in this case. If you have a doubt, plan to get married immediately at the earliest. Hope you have observed some of the similar situations in day-to-day news that girls who got cheated in the myth of getting married with a person are filing cases and coming on to roads performing strikes demanding to get married with the guy who has cheated her in the name of love and promise of marriage.
Love or a promise to marry cannot be made into contract.
Moreover, personally speaking if you ask for such written agreements in such sensitive issues, the 2nd party would get a feel that you don't believe him and that in future you may harass doubting him everytime on every thing. This paves way for misunderstandings and seperation.
So, it would be better to inform your parents and get engaged at the earliest.