I was thinking that since baby's in bed by 6:30 pm, 5:00 am wake up is pretty normal. How about a later bedtime, see if she then sleeps later in the am, thus postponing the bm until later?
It's always something. My two monkeys are waking up because the heater's cycling on in the early morning now that the weather's changed. Well, jeez, can't turn off the heat boys! Just gotta adjust to it. Maybe your baby needs an adjustment too... I'd do a later bedtime, personally if it's feasible for your family and her routine.