A hat or bonnet was necessary outdoor wear for women and girls. Although historically accurate, beautiful, hats and bonnets can be purchased from costume vendors and professional milliners (including those at the Dickens Fair), they are expensive. You can’t make a *great* hat or bonnet without study, training and a lot of work, but you can approximate a *pretty good* one with patience and a bit of handiness!
Look for thrift store and discount store hats that are made of wool felt, in a boater (narrow brim, flat crown), picture hat (wide brim, round crown) or pillbox (flat crown, no brim) shape. Ladies' "church hats" are useful for this. Take off all the modern trim, which will probably be hot-glued on. Feel free to cut your hat to make it the right shape (cover the cut edges with ribbon sewn or hot-glued on top). If the brim of the hat is large enough, you can cut off the back of the brim (behind your head), and fasten long ribbons to each side (tie them under your chin) to make it into more of a bonnet shape. If you know how to use the steam function on your iron, you can steam the felt until it's damp, re-shape it over a bowl or something that's the shape you want, and let it dry to have a better bonnet shape. This can be tricky, though, so make sure you have time to fiddle with it and practice before you need to wear the thing!
You can also cut the entire brim off of your hat, just leaving the crown, as a pillbox style hat. Some stores (like Target) sell pillbox style hats in fake fur that will look good as-is, if you just pin, glue, or sew a feather and ribbon bow on one side or the front. If all you can find is an old straw hat, be sure to hot-glue or sew some fabric over it so that no straw shows. Solid, dark-colored velvet, corduroy, wool, or thick flannel with no printed design will work for this; shape the fabric to the straw hat with pleats, making the pleats look as nice and smooth as you can, and hot-glue, safety pin or sew it in place, fastening the edges to the inside of the hat.
Decorate your hat with ribbon, silk flowers, feathers, etc. to coordinate with your costume (it doesn’t have to match all the colors exactly), fastening the ornaments on with straight pins, safety pins, hot glue or needle and thread. Bonnets had trim edging the brim, on the sides over each ear, in a line from ear to ear over the top of the bonnet, along the back neck edge, and inside the brim framing the face. Keep your hat or bonnet on your head with a proper hat pin (like a straight pin, but 5 to 10 inches long) stuck through the hat on one side, through your hair inside the hat, and through the other side of the hat, or with small plastic combs sewn into the inside of the hat. Pillbox hats and bonnets should have long ribbon ties securely fastened (sewn or safety-pinned) to the inside, over each ear, to tie under the chin when worn. These ribbons should coordinate with the other trimmings on your hat or bonnet.