That was a super tough age for us and we went through this waking up to play phase too, except my girl did it between 2 am and 5 am. A few things that helped:
- make sure she gets rest during the day. We had big problems trying to get DD to nap at that age. We had to install blackout drapes and use a fan for white noise and those helped her nap and sleep better at night.
- until she grew out of this phase, I'd pick her up and put her on the floor with a couple of quiet toys and let her crawl/cruise around while I lay down on the floor, resting. The lights stayed off and she would entertain herself for a bit, then fuss, so I'd nurse her again and try to get her back to sleep. If she resisted, I'd again let her play on the floor, lay down and try again later. In a couple of weeks she went back to going straight down to sleep again after waking and nursing. By keeping everything dark and boring at night, she did get the message that it wasn't fun to be up at night. Other than that we simply had to ride it out. She has had sleep setbacks with every major developmental milestone and 11 months was huge: working on walking and talking at the same time. She was waking up, trying to practice her skills and not being able to shut her little brain down.
I hope that helps, right around one was the toughest age for us yet - she's 27 months now.