For the duster, or duster analogue, you could look into something like an oilskin or canvas trench coat - you may need to make your own, since most women's trench coats are decidedly not oil skin. He doesn't get the leather duster until halfway through the first book, if I am remembering right, and prior to that, he wore a canvas duster. It'll still be a bit warm, but you'd be able to take it off when outside, at least.
And oh, that hat. Cover artists run rampant - he makes at least two references in the book to "I don't do hats" - but it is iconically associated with him. I'd be careful with getting the smaller fedoras - they have a different shape from what Harry wears, and could confuse the look potentially. Most have a curved and indented top, while Harry wears one that is almost completely flat across the top - finding a small one like that may be tricky.
But - a lot of what makes Dresden identifiable is the details and accessories. The Sheild bracelet, the pentacle, the rings, and the staff. All little things, but when added up, they can make a gender bent costume that more recognizable. Also, bonus, the staff can double as a hat and coat rack when it gets too warm.
Good luck! I can't wait to see what you come up with