Without taking anything away from Captain Warner, Wikipedia says it was Helen Richey in 1934, for Pennsylvania Central airlines. She was booted from the cockpit by the then-all-male pilot's union sometime thereafter. In another place, Wiki recognizes an un-named American Airlines first officer the same year (1973) Ms Warner signed on with (old) Frontier as a first. Someplace in my memory, I remembered the first female as being at United, but can't document it.
Certainly one of the too-long-protected domains of male exclusivity.