When Doomfist arrived last week he was quarantined from Competitive Play in order to give everyone a bit of time to adjust to his presence. Well, I sure do hope you've managed to just that because the floodgates have now opened and Doomfist has been unleashed upon Competitive Play!
I've only had the time to play a couple of mid-GM games with and against him, so take the following with a few grains of salt, but I'm pretty certain that he's not going to mingle well with the overly popular dive teams. In order to achieve any sort of mobility Doomfist needs to sacrifice his defensive cooldowns, which as you might imagine makes him quite vulnerable in close quarters combat. So despite his tag saying "offense" I believe Doomfist is going to be much better at defense, especially when it comes to protecting healers from pesky scientists and robot ninjas.
As far as tips are concerned, the most important thing you need to keep in mind is to not overextend! Doomfist might appear quite tanky on first glance, but all of that health quickly melts away due to his rather large hitbox. So let your tanks initiate the fight, and then start cleaning the enemy team up amidst the chaos. Just make sure not to charge without a target in mind as that's a surefire way to get yourself unceremoniously killed. Oh, and if you didn't already know this, you can cancel the Rocket Punch by simply left clicking (primary fire) - you won't even lose ammo!
The second and final thing you'll need to seriously work on is aiming. Doomfist's shotgun is more of a wet noodle-launcher given the slow speed of its projectiles, but it does a surprising amount of damage when you do actually hit. So take a bit of time to really get used to the projectile spread and speed, because pretty much all of Doomfist's combos rely on weaving in a constant barrage of shotgun blasts. You really don't want to end up in a situation where you use all of your cooldowns to almost kill someone, only to die before finishing the job.
Have fun, but please first learn how to play him in Quick Play before heading into Competitive! Doomfist is by no means an easy hero to play, so give him and your team the respect they deserve.