I have flown Webjet once before on their ancient 737-300. Having the last week Southwest incident in mind, should I be worried? I have a flight later today...
I don't think so. The 737-300s aren't so old compared to other narrow-body jet passenger aircraft in use today. The problem with Southwest is that their typically relatively short flights and especially thirty-minute turnarounds mean that the Southwest planes are used extremely intensively. The number of cycles rather than chronological age or even total hours of flight time is generally responsible for the stress that aircraft experience.
We're glad to know that you're fine, albeit a bit annoyed about the plane you rode today. Do you have a return flight on a 737 in your near future?
No, I went by road from SDU to GRU, and flew back. But I might very well fly 737 in the near future. Nothing booked yet, though... Not a big fan of Webjet, but for a 0h45m flight, and when the price is way cheaper than the competitors, and they are the only carrier between these two preferred airports in SAO and RIO, then I find them the better choice.
The Webjet fleet is quite young by 737-300 standards, averaging under 20 years old. They came from many sources but a fair number are ex-UA aircraft. All of them are fairly low in cycles by 737-300 standards and all of them had major inspections as Webjet acquired them. I don't much like ancient aircraft but I would worry less about those than the ancient MD and B products with Delta, US Airways and Southwest, among others. here are a few fleet details: http://www.planespotters.net/Airline/Webjet-Linhas-Aereas