Of course parsing is something thats very important if you are making your own DSL. And this is another application where Haskell really shines. This is why the guys who do programming language research produce papers with code in Haskell. Its orders of magnitude easier to make your toy language for exploring evaluation order in Haskell than it is to do the same in Java.
Its easier to learn a language if you're building something you're interested in though. Personally, I learnt a lot of Haskell implementing a web app with Yesod[2].
Good luck.
[1] http://book.realworldhaskell.org/read/using-parsec.html [2] http://www.yesodweb.com/