Katherine Schwarzenegger Proves Her Love for Chris Pratt with Airport Run

Chris Pratt and Katherine Schwarzenegger will be together forever -- it's an absolute lock, and we know this because she did something for him early Friday morning ... that almost NO one in L.A. does.

Ya probably wouldn't believe this if we didn't get it on video, but here it is -- Katherine behind the wheel at 7 AM, driving her fiance and dropping him off at LAX!! If you live in L.A., or even if you've flown here, you know the airport is an absolute nightmare.

Kat stayed in the car as we congratulated Chris on their engagement, and chatted about a possible best man for their wedding. You gotta see him, because the smile on Chris' face screams one thing: My girl will do ANYTHING for me.

We got even more proof they're rock solid on Thursday night ... as the couple did dinner with Katherine's mom and brother -- Maria Shriver and Chris Schwarzenegger -- and Pratt's son, Jack.

The goodbye scene outside the Smoke House Restaurant in Burbank was straight out of a Hallmark card. Jack had big hugs for Katherine's bro and also for Nana Maria.

Super sweet ... but still pales in comparison to the scene at LAX.