Dole out is a phrasal verb meaning to administer or bestow, especially in small portions. It is sometimes misspelled doll out, which has no logical meaning as a phrasal verb (though of course it does work in in rare constructions such as she threw the doll out). Doll does appear in the phrasal verb doll up, but its meaning has nothing to do with doling out. It mean (1) to dress for a special occasion, or (2) to add embellishing details.
Dole out is sometimes misspelled doll out—for example:
She suggested allowing council members to doll out rewards … to city staffers. [Voice of OC]
The discipline dolled out by the Sisters was very strict, with a 10pm curfew for all their intern students. [Prince Albert Daily Herald]
These writers spell the phrasal verb correctly:
Most legislators divvy them up into one-year scholarships so they can dole out eight of those in a single year. [Belleville News Democrat]
Owners would like to be able to dole out less expensive contracts, but they wouldn’t want to sacrifice their added revenue. [Los Angeles Times]
There is also a question over who will dole out funds. [Telegraph]