The basic idea is to log the time when a group starts a dungeon, and then log the time again when the same group kills the last boss of that dungeon. It's just a simple subtraction to figure out how long it took them to rush to the end, and then the best times and the group members can be displayed on the website in a nice leaderboard for each dungeon.
Really simple rules: the timer is canceled if anyone leaves the dungeon, but the group can continue even if some members die. I am not sure if there is a need for any other reward than just sitting on top of the scores. If anything, maybe some potions to compensate the ones needed for the runs or simply some golds. Because it pushes the groups to their limits, death will happen a lot and this may turn into a very expensive activity.

I suggest this because the main reason people quit MMOs is simply boredom, or lack of exciting things to do, especially for hardcore gamers who tend to play a lot and not only log in for "raid night". And here we're talking about a 10 years old game with absolutely no surprises left in it, with dozens of complete guides about anything already available... I think this is a different approach to a rather boring activity in 1.12 that would hopefully entertain the most active players more than just sitting on their butt in Org and IF, or even attract some new players with a strong competitive spirit.
And there is plenty of elements in the game to make this thing interesting. Ideally, people will start recording runs (gathering some views for the server!), discuss together the best strategies and we will bring the fine art of speedrunning into WoW 1.12! Or not. Either way, I believe this kind of feature would make the server more attractive, and this will be my last point.