Dear Lara,
Thanks for your question. Please kindly be advised that it is possible to hire a private car from Xiamen to Nanjing. To be honest, after the Covid-19, private tour or private transfer (car hire) is the best way to travel in China in 2021.
As you know the risk-level of all cities in China has already been low-risky, for Chinese and all the expats living in China, 2021 will be a good time to travel around China. Although it become less risky to be infected by the COVID-19, we still need to make enough self-protection, such as not gethering, travel with mask. Of course, traveling by a private vehicle is necessary while you are traveling arround China this year.
For a small group of 2 people, a private 5-seat car is a good choice. Hiring a 5-seat private car with only driver service from Xiamen to visit Nanjing Tulou, with a back drive to Xiamen after the visit in the afternoon, the rental fee is about $275-300 per car per day.
Suggesting itinerary:
Morning hotel pick up - 3 hours driving - Nanjing (visit Tianluokeng or Snail Pit Tulou Group + Yuchang Building + Taxia Village) - 3 hours driving - Back to your hotel in Xiamen
Hope the above information is helpful. :)