I asked the very same question a month ago ^^
I've been told the Dragon is a lv30 monster so it i guess it might be possible to wack it. BUT the dark dragon is not alone.
Another monster called searcher is here too.
I can help you if you want. I'm not online very often due to tons of work in real life ^^
The only problem I see with soloing it is the curse it can bestow on you which acts much like rez sickness...where your max HP and MP are decreased to like... 1/5 of the original value... >_<
just beat it, paid a level 60 white mage 2000 gil to help me out lol, but he even teleported me back to konschat after it was over so it guess it was all worth it