I do it the same way that you do almost every day. Cardio before breakfast at 5:45 am (OK, I'm a little early than you are!) and weights in the afternoon.
The advice to do weights first, then cardio is only referring to when you're doing them in the same workout, with no time off between the two. When you split them up the way that we do, you eat a meal or two and your muscles get to recuperate in between workouts.
Some experts think that splitting up weights and cardio has a beneficial effect on your metabolism because you're boosting your heart rate twice in the same day. Of course, a lot of people just don't have time to split up exercise. But if you can do it, go ahead and do either one first in the morning and the other later in the afternoon.
Have fun!