I was actually wondering, since she's out West, if this would have been something she could have worn into town?
http://www.cattlekate.com/store/womans-western-wear/casual-western-wear/ingalls-1800-skirt
Does that make any sense?
No. That's not historic at all. (And looks darned difficult to ride in.)
There are good books out there of nineteenth century general American and Native American costume (Texas Tech University Press has put some good ones out). Also many excellent museum collections.
But as a crash course on the parts I'm more familiar with:
No bras. Bras are a twentieth century invention.
Corsets were available mail order. They were always worn over a chemise since they were not washable. A chemise looks pretty much like a sleeveless white cotton nightgown. There was sometimes another layer of underwear over that like a very fitted white cotton nightgown before the actual dress went on, and there was always at least one petticoat.
Corsets provide plenty of bust support -- better than bras, actually. While they were laced up the back, by the mid-late nineteenth century they also often had patented quick-release "busks" in front so the lacing could be left alone.
Most corsets were made of tough utility canvas fabrics.
Many Victorian women went commando under the dresses. Underpants are another twentieth-century invention, and anything else was difficult to manoeuvre in under the skirts in the toilet.
Judging from old photos of pioneer women, some would forego corsets entirely. But just about everyone older than a teenager wore headgear whenever she set foot outside the house -- a sunbonnet, if nothing else, but always a hat, bonnet, or flowery frou-frou of some kind, never a bare head. It was considered a little shocking and unorthodox to do otherwise.