Thanks, all, for your quick replies! Appreciate your comments. We will have to think positive and cross fingers tightly then - for no delays and for good weather!
Our flight out of LAX is very early (6am - which is the first flight of the day LAX to DEN), and I will book to stay the night before at an airport hotel.
I don't have any status with United - but a frequent flyer with Qantas. I booked on United to fly to Omaha via Denver from LA because the flights take less time than going with American via Dallas Fort Worth. It is for the convenience.