In a sweet selfie shared by Kloss, the supermodel and her husband comfortably leaned their heads together during what appears to be a safari ride.
The couple, who dated for six years before getting engaged, both wore white tops for the outdoor excursion, though the Project Runway host accessorized her look with a red scarf and gold hoop earrings.
Not only has the Christmas trip been a fun adventure for the couple, but it's also brought them closer to nature.
In the first image shared by Kloss from the vacation, she stood peaceful in an infinity pool as she watched an elephant walk past her.
She also posted a photo of a yawning, sleepy lion, which she humorously captioned, "Mood." Additionally, she expressed her joy to fans in an Instagram Story video on Wednesday after seeing a large family of elephants. In the footage, she turned the camera to her face and mouthed, "Oh my God."
Meanwhile, Kushner, 33, opted to show off his photography skills on Tuesday by sharing a smizing picture of Kloss wearing a straw hat and floral ensemble with white flowers. "South Africa," he captioned the shot.
"The wedding was intimate and moving. The couple was beaming with happiness," a friend who attended the ceremony told People.
The pair announced their engagement in July, weeks after Kushner popped the question during a romantic weekend in upstate New York. "They're both overjoyed and happily celebrating," a source close to the couple told PEOPLE at the time. "Their hearts are full and they're excited to build their future together."
Kushner proposed with a high-carat cushion cut diamond in a platinum solitaire setting with a diamond pavé band.
When Kloss shared the news of their engagement on Instagram with a sunset selfie kissing Kushner, she wrote: "I love you more than I have words to express. Josh, you're my best friend and my soulmate. I can't wait for forever together. Yes a million times over."
Prior to their engagement, a source told People that Kloss converted to Judaism in early June. "She's never been one to make decisions lightly," the source said. "She spends a lot of time reflecting and learning."