Hello Seria,
I used the website tool "Town Search" on the JewishGen website and entered Carlsrad with a Soundex search.
http://www.jewishgen.org/Communities/LocTown.asp
One of the results was Karlsrode, which I think might be the one you are looking for. It is not in Hannover, but located between Göttingen and Leipzig. Go to Google Maps
http://maps.google.com
and for the location, cut and paste this:
Karlsrode Dietersdorf, Sangerhausen, Saxony-Anhalt, Germany
Then click search. Then zoom out.
Directly north of Karlsrode about 20-25 miles is a town named Halberstadt (possibly your Herbstadt?).