The Swans confounded expectations of a rapid return to the Championship by finishing 11th in their maiden Premier League campaign.
The Welsh club won plenty of plaudits for their attractive passing style but have had an unsettling summer with Brendan Rodgers and Joe Allen departing for Liverpool.
Laudrup is the man tasked with carrying on the Northern Irishman's good work and has strengthened his squad with the arrivals of Michu, Chico Flores, Jonathan de Guzman and Itay Shechter.
But the loss of Rodgers and the dreaded 'second season syndrome' mean many are again tipping Swansea for relegation.
Laudrup said: "I have read in the last couple of weeks a lot of experts saying Swansea are one of the favourites to be relegated, because the second season is more difficult than the first
"I agree that the second season is more difficult but we have to prove these experts wrong. We have a good team, we have brought in players with experience of the highest level and we just have to show that they are wrong.
"We want to show everybody that Swansea is not just a club passing by, it's a club that wants to stay at the highest level for many years and that's a huge ambition to have.
"There are clubs in the divisions below us who want our place, we know it's a huge challenge but we are ready for it."
The Dane has been linked with further additions to his squad, including Valencia winger Pablo Hernandez and Preston's Jamie Proctor.
But Laudrup, as he has through the summer, remained tight-lipped on whether he had made bids for either player.
"I will say what I have said already, when things are done one way or the other then we can discuss it," he said.
"We are still on the rumour level, sometimes there are talks and we want to strengthen, but until things are certain we can only talk about players that are here now as they are the most important, they are the players we can count on."
Swansea head to Loftus Road having never won a league game there, and they have suffered heavy defeats on their previous two trips to face the Rs.
But Laudrup feels that will have little meaning come kick-off.
"I don't pay attention to statistics," he said. "I have seen that we do not do that well when we play at QPR but statistics; they are only numbers on a piece of paper."