From Smith's Dictionary of Greek and Roman Antiquities, entry for Matrimonium:

Towards the close of the republic it had become customary to betroth young girls when they were yet children; Augustus therefore limited the time during which a man was allowed to continue betrothed to a girl (Suet. Aug. 34), and forbade men to be betrothed to girls before the latter had completed their tenth year, so that the age of pubertas being twelve years, a girl might not be compelled to be betrothed longer than two years (Dion Cass. LIV. p609, Steph.)

and

...as the foundation of the notion of pubertas was physical capacity for sexual intercourse, there could be no pubertas if there was a physical incapacity.

I offer no opinion on what is meant by physical capacity for sexual intercourse and simply note that even the law of Augustus leaves open the possibility that a girl might be married at age 12.