If she doesn't absolutely need to arrive in Tainan that night I think overnighting at the Novotel or other option near the airport and taking a train the next morning is probably most sensible.

As noted the Tainan HSR station is a ways out of town so arriving there very late at night and then finding a way into town might or might not be an issue. There's a local train shuttle that runs between the HSR station and the main station in town which is fairly cheap and easy, but I don't know for sure the operating hours. I suspect you could get a taxi though without too much trouble.