There is no such word, but you might have mistaken 돌반지 for 몰반지 (they can look similar). 돌반지 = 돌(birth anniversary - unrelated to "stone") + 반지(ring) => birth anniversary ring for babies. On the first birthday of a baby, many parents have a gold ring made for it since it's such a joyous occasion (in the old days infant death rate was high). They also commonly have a party called 돌잔치 inviting friends and relatives and taking pictures of the baby in nice clothes. 돌 is the unit of counting a baby's age by the number of full years (한 돌 됐다. 두 돌 지났다), since 살 (한 살, 두 살) doesn't reflect the true biological age.

l've never heard that word for all of my life in korea