to augment the idea that she may be hungry or thirsty - you can leave a sippy cup of water in the crib so she can help herself if she wakes up. (I suppose she may not be old enough to understand that yet, but, it seems like good advice as kids get older.)
It seems like you should try to get her back to sleep in her own bed - maybe go through a shortened, modified, bedtime routine, and then put her back into bed? I notice that my little girl no longer falls asleep so easily in my bed, and generally have better luck putting her back into her bed if i think she is still tired. The more interaction she has with me, the more she seems to think it is time to get up. So maybe that would help?
(It is harder, because you have to sit up for a little while in her room, but, it seems to me that in the long run i have gotten more sleep this way - not less.)
BTW, most of the sleep advice i read suggested that you needed multiple nights of an approach to get it to really work, and often the first couple of nights are harder, not easier. So don't be too discouraged if whatever you end up trying takes more than one night.