We've flown cross-country (or near to) on United (formerly Continental) with DD and have had no issues. I also have a bit of airplane anxiety - I'm most anxious while taxiing to the runway or jetway - and have flown on larger planes as well as smaller planes (think EWR to Toronto)
I prefer larger planes, but the ones in United's fleet are fine. If you select United, I do recommend trying to get into the "Economy Plus" seating if available - the seats have more legroom than the standard coach seats, which helps if your DD gets antsy like mine does. It does cost a bit more than regular Economy (Coach) seating, but it's worth the spend.