The happy couple flew out from Gatwick airport on Friday and touched down in Tanzania where they have had a jam-packed four days on the Selous Game Reserve in the south of the country.
They previously had a mini-moon in Croatia, immediately after their white wedding in Montenegro in September.
Hannah and her Serbian other-half are also marking seven years together this month, making their romantic getaway all the more special.
The loved-up pair weren't looking to sit around the pool though as they have had an adventurous week so far, going on safari and soaking up the wilds of the reserve together.
Daring Hannah also took in the breathtaking views of the area on a light aircraft, joking on social media that she may as well have been a co-pilot on the excursion, she was so enthusiastic.
"Tanzania you have my heart already," she said.
"I have been in awe since arriving in this beautiful country and the sunsets are out of this world. Just call us the Wild Thornberrys," she added.
"We had an incredible game drive in the Selous reserve and got so lucky seeing a dozen elephants, hundreds of giraffes, three lionesses, hippos, zebra, the list goes on. Bring on more tomorrow."
The Dublin model and Nemanja have recently bought a place together in London, where Hannah has kept up the successful modelling career she forged with the Andrea Roche Agency here.
The next stop on their journey is Zanzibar island, where they plan to scuba-dive and enjoy some down time.