Can DNA be used directly to determine the age of a mutation?
Yes, you are right.  Proteins are specified by DNA sequences, so DNA sequencing is a more direct way to obtain essentially the same information.  Note that mutation dating via DNA or proteins is approximate.  It involves a lot of assumptions about continuous rates of mutation, but in fact mutation is a stochastic process and does not have a knowable continuous rate.  The sequence of mutations can be determined with high confidence, but the rate can only be determined approximately.