L.M.
Hi there. My LO did the same thing yours is doing, but started a little later - more like 6 1/2 months.
I too thought she was hungry, but when I started feeding her and she did not go back to sleep, I knew it was not hunger. Also if she is playing and then gets upset I doubt it is hunger otherwise she would be crying - get me some food now!
So, this is what we did:
At 4:00am when she typically woke my husband went in there and repeated her night time routine, a shortened version and minus the feed. He usually puts her to bed anyways, and since I breastfeed I did not want her to think it was a feeding time.
The routine for us: He got her out of her crib, sat with her in her rocking chair for 5 min, then put her back in her crib, gave her her blankie, turned on her music box and left the room. If she got upset after he left he went back in and sat in her rocking chair and just talked to her - no feed, no more picking her up. It took NINETY minutes the first night! Then it got less and less.
We also make sure that she is crying before we go in and not just fussing. Sometimes she'll fall back asleep before she ever gets to the crying part.
Try your night time routine in the middle of the night, and try feeding her as close to bedtime as possible.
GOOD luck!