American Airlines Virtual

Since you are flying offline and practically in uncontrolled airspace (which would never happen at DFW except during a zombie apocalypse maybe), what I would suggest is to make the turn as required to 030/130 until you are clear of any other departing traffic, then turn DCT to your first fix. Personally, I would tune the TTT VOR and wait to make my turn until 7-10 miles out. That is just a personal preference though. "The book" might say something different.

I would guess the 030/130 deg turns are to get the slow turbo traffic away from the runway center line as soon as possible thus not delaying faster jet traffic departing (that will follow the center line for a longer distance). So once you clear the runway threshold I'd start my turn.

Normally when flying online ATC will vector you to the first or more often direct to the second waypoint. So clear the end of the runway and head to the most convenient waypoint (or radial to a waypoint) based on your position.