Travel Rothenburg to Prague

Deutsche Bahn has a schedule on a Friday night ( I plugged in March 25 for example) at 22:09 hours that arrives in Prague Main station the next morning at 10.54 with 3 changes. You did not mention a month or date, but you could look at www.bahn.com to see the schedules, prices and more.
Viamichelin.com has driving times of 380 km and 3 hours 37 minutes ( add 25 % to that for real time) if you find a car you can take to Eastern Europe safely.

A common misconception about travel in Europe is that there are somehow night trains between everywhere. Not true. And with day trains becoming faster, night trains are becoming less common. Rothenburg is not that far from Nürnberg and there is now a Bahn bus that makes the trip from Nürnberg to Prague almost non-stop in about 3½ hrs. With advance purchase that trip can be as low as €19 pP.

For €33, up to five people can travel from anywhere in Bavaria to places inside the Czech Republic using a Bayern-Böhmen Ticket. The Bayern-Böhmen Ticket is similar to the Bayern-Ticket - all day, on-off, regional trains, after 9 AM workdays - except it includes a section of the Czech Republic (pg 2, blue lines) near the border, including Pilsen (Plzen). There are four 5-hr direct or one-stop trains from Nürnberg to Prague per day. The trains go through Pilsen, so you can use your Bayern-Böhmen Ticket from Nürnberg to Pilsen (after using it from anywhere in Bavaria to Nürnberg). The fare from Pilsen to Prague is 147 Koruna (about €6) per person. I'm told you can buy the ticket from the Czech conductor on the train (might need Koruna) and not have to get off in Pilsen.