Generally DBeaver should work with Java 1.6. Even with OpenJDK. I guess problem is in something else. Could you check for log file(s) in ${user.home}/.dbeaver folder? If it is not there then probably it is in DBeaver installation/configuration folder.
Debug log is for very specific purposes. Please check for log files in .metadata folder. These log files are created by Eclipse framework and may have quite weird names but in any case they have extension "log".