The two oldest parts of the Bible are associated with women (The Nerd listened to Richard Friedman giving a talk on this at SBL in 2014). One evidence of their ancientness is the archaic Hebrew found in both passages.
In the first, Miriam, sister of Moses, took up the ‘Song of the Sea’ (Exodus 15:20). The other seems to have been composed by Deborah, the ancient poem in Judges 5.
These texts have signs of being an older form of Hebrew. There are various sources behind the edited work known as the Torah or Pentateuch and even the sources (J, E, D, P) had sources (genealogies, epic poems, king lists, etc.). The ‘Song of the Sea’ is part of the J source which was composed sometime between 848 and 722 BCE in Judah (sometime between the reign of Jehoram [848-841] and Ahaz [732-716]). (See Richard Friedman’s Who Wrote the Bible? to understand the “documentary hypothesis” of the origin of Torah).
But the Hebrew of ‘The Song of the Sea’ has features (including references to a lost epic poem about God’s victory over the waters of chaos, see Umberto Cassuto’s commentary for more) indicating that it is much older. It appears to be from an earlier time period than the narratives around it.