Do you mean Velden am Woerther See, near Klagenfurt and Villach? Rome2Rio gives a variety of options, the fastest of which is to drive. But that would probably be extremely costly because of the drop charge usually assessed on cross-border rentals. You could check with AutoEurope, Kemwel and Gemut, though, to see what sort of rental rates they can offer. I imagine you'd need to go to either Klagenfurt or Villach to pick up the car, and dealing with a car-rental agency on both ends of the drive would take some time. In the end, the car-rental route might not actually be faster.
The next-best option looks like the train. There are several morning departures (with varying numbers of connections required) that will get you to Budapest 7 to 8 hours later.
Edited to add: That's a long train trip, and I'd guess potentially costly if you wait till shortly before your travel date to buy the tickets. If you are absolutely certain about the timing of the trip, buying the tickets when they first become available for your travel date may yield very nice savings. The bargain tickets are often non-changeable/non-refundable, so you need to be certain about your travel plans before making the purchase.