An Irishwoman is a woman from Ireland, or a woman who is Irish. It is Irish + woman, built the same way as Irishman. The meaning is clear, but the one-word form is a little formal or old-fashioned in tone; “an Irish woman” as two words is also fine, and often sounds more ordinary today. Use it only for a woman. Keep the capital I. Though actually, as with Irishman, many people would rather you just say she is Irish, and name the person, not the type.