I've ridden in Dallas and I KNOW it's got hills. Lots of hills.
I'm sure that you like your new bike and I applaud you for taking the initiative to get in better shape. Sometime in the future, you might want to consider getting a bike with gears to make the hill climbing easier. That would also widen your horizons in terms of areas where you can ride.
Anyway, have a good time on your bike and keep us posted on how it's going!