Has anyone flown this route Before using the 737-900
No, but I’ve done KDEN-PANC, KSEA-PANC, and KMSP-PANC. You might need a little larger plane from KIAH.
You should be able to do IAH-ANC in a B739 - I’ve done DCA-ANC just fine and that’s a similar if not longer distance.
Aircraft wise, I think you can do it.
Realistic livery wise, you’d want a United 757-200 (or 737 MAX but we don’t have a MAX yet)