I'm pretty sure that most moderate-complementarian churches allow women to hold the position of head worship leader, but since enough complementarian churches do not, and Miriam is the first woman in scripture to be given the title prophetess, her story is worth telling.
Miriam, sister of Aaron and Moses, is called a prophetess (Exodus 15:20) and leader (Micah 6:4).
God declares through Micah that He sent "Moses to lead you [Israel], and also Aaron and Miriam."
Miriam also leads the Israelites in their first service of worship as a free people. At first glance, the text would appear to indicate that Miriam is only leading other women, but that is because of our sometimes limited English language.
Shawna R.B. Atteberry of The Voice: Biblical and Theological Resources For Growing Christians provides a textual analysis based on the original language:
Just another example of a woman of God leading both men and women.