Upvote:11
(The maps are from an Atlas Obscura article on Isochronic maps and the wikipedia entry on German Railways.)
Here's an isochronic map centered on London from the early 1880s to give a feel of how long it would take ~20 years later:
The German rail network in 1861 suggests there already was a track nearby (you can see a track between Eisenach and Bamberg if you zoom in) so the travel time would likely have been within 10 days in 1862 as well:
For completeness, the travel times in 1914 to illustrate how fast things evolved back then: