Hi R.,
Kudos on running! I admire and envy you. I was a runner in my past life, but can't seem to regain my motivation...maybe you can help ME with that! ;-)
I ALWAYS wake my son to feed him. While I am sure this is just a personal choice you will have to make, do what works best for you. My son was in NICU for two weeks where they put him on a strict feeding schedule. One of the feedings was around midnight. I found that when we got him home if I woke him for that feeding (sounds like I am talking about an animal-- just don't know what else to call it), anyway, if we wake him to feed him at midnight then he sleeps until 5 am which works great for me. I am a morning person, so I don't mind the 5. My husband is a night owl, so he does the midnight thing while I sleep. It also gives my hubby his "alone time" with the baby to cuddle and coo. It works great for us, but others would say we are crazy!
Also, you could try pumping a few ounces out before you leave and put it in the fridge. If she needs it, then it is there. If you really enjoy that morning feeding time with her, then don't pump enough to fill her up, just enough to hold her over until you get home.
Good luck and happy running!