You show a lot of commitment by not having a single drop of alcohol for 6 months and changing your lifestyle by going to the gym and eating well. This will definitely improve your overall health and help to flush out alcohol in your liver. However depending on the previous level of alcohol abuse, the length of time to clear out your system will vary accordingly but your GP should be able to tell you how you are doing if you ask about your progress.
Fingers crossed, you should get a positive reply back. Anyway good luck and let us know how your test went.