09/15/2012 at 12:45 PM EDT
and Duchess of Cambridge
are hanging in there.
Even as more photos of Kate sunbathing topless are published in the Irish Daily Star
and news comes that Italian magazine Chi plans to follow suit
, the royal couple, who expressed their anger over the publication of similar photos
of Kate on Friday, are moving ahead with their tour of Southeast Asia Saturday in the rainforests of Borneo.
"Their royal highnesses are feeling upbeat, they are enjoying the tour and they will not in any way allow what has happened in France to overshadow the tour and their work on behalf of The Queen," a palace source tells PEOPLE of the couple's mood.
After traveling to Sabah, one of the two states that make up the Malaysian part of Borneo, the couple arrived Saturday by government helicopter to the Danum Valley, where they met with Malaysian and British scientists.
Then they were fitted with harnesses and hoisted 130 ft. up a rainforest tree.
"I'm going to go 'whee' and just fly up," Kate joked.
William was also in a playful mood: "Girls don't have the same wardrobe malfunctions as men do," he said as he waited to be pulled up the tree in his harness. "I hope I don't have any wardrobe malfunctions."
At the top of the tree they met with Kalsum Yusah, 32, from Sabah, who completed a PhD in entomology at Cambridge University and is stationed in the forest.
"They just said it was such a surreal, totally unique experience up there because they had never been up in the canopy," she said. "They enjoyed it immensely and they weren't scared of the heights. They asked about the primates, birds and insects, and they were interested in how the forest is sustained."
According to the palace source, the couple are determine to enjoy themselves despite the distraction of the photos published by French magazine Closer
, which a St. James's Palace spokesman called "grotesque and totally unjustifiable."
"The tour has been organized to celebrate Her Majesty's Diamond Jubilee, and tens of thousands of people have already used the occasion to pay joyful tribute to her reign," the palace source said Saturday. "Their royal highnesses will not allow this story in any way to dampen that heartfelt and genuine enthusiasm."