I agree with Greenbaum's advice, excellent as always. There is simply no way to count on being through immigration and customs in under 2-3 hours. One might get very lucky. But it is unlikely.
There are some good web sites for shopping for fares, such as Kayak. By checking every few days, one can get a sense of a good fare. Once one knows what a good fare is, one can buy with confidence. There is nothing wrong with buying with cash. But buying with a credit card from the U.S. can give some consumer protections in case things go wrong.
If the ticket is already purchased, I would not change it. United has 6 non-stops a day from SFO to AUS (Austin). If your fiance misses her flight, United would just switch her to the next flight, assuming there is room.
Also, realize that arrival times across the Pacific (in either direction) are quite wind/weather dependent. If she arrives 1-2 hours early (due to good tail winds), she might well make the original connection. If she arrives late (due to lack of tail winds), she could land after the scheduled connection takes off.