You probably won't be able to find any civil records, sind civil registry offices in Germany weren't established before1875.
The church records of Dresden have been put on microfilm an can be searched at:
Since you live so far away, maybe the employees would be willing to conduct the search for you - you might want to inquire about that (an inquiry should be written in German). Keep in mind though, that they will charge you for their services by the hour (and it won't be cheap). A big city such as Dresden had more than one church, If you can't give more detailed information, a search may take quite some time, provided they are willing to search at all.