Proper course of action when car engine suddenly dies occasionally when car is stopped

When I was driving home from work today I stopped at a traffic light. The car was stopped and in drive, and my foot was on the brake. I was on relatively level ground, and the ground was relatively smooth (no debris). The engine was not hot, and it was during a cool night.

I noticed that the engine turned quicker than usual a couple of times: the RPM meter showed that the engine was turning slightly over 1000 RPM (even though the car was stationary and my foot was on the brakes) for a couple of times, then the engine suddenly turned off (the display was lit, but the car would not accelerate if I lifted my foot off of the pedal while in drive). I was able to move the gear-shift to park, turn off the battery and ignition, then turn the ignition, battery, and engine on successfully. I didn't encounter any more issues on the way home.

This is the second time I experienced this issue. The first time was last week, and the conditions were the same.

I drive a 2003 Lexus RX300. The engine was last replaced in November (a little over 3 months ago).

Is this sufficient evidence to warrant seeking auto-repair? If so, what should I reasonably expect?

I can provide more information on request. Thank you 🙂

EDIT: Title change.