DME runs all day/all night...as long as there is a need to get guests to and from the resorts, to and from the airport. For a 7:15am flight, you would be given a p/u time of about 4:15ish...give or take about 15 mins either way, depending on your resort.
And yes, even at that time of day, you need that time. You should plan to be at MCO no less than 2 hrs prior to departure. So, that 3 hrs may seem excessively early but it really isn't. Plan to grab a bite to eat at the airport.