Hi A.- just remember the saying, "this too shall pass". It will pass and you will eventually be able to get a good nights sleep. The whole first year after my 2nd arrived, I was horribly sleep deprived. It was always something - the 4yr old wet the bed or was too hot or was thirsty or the little one threw up or was teething or his toe was stuck in a little hole in his footy pajamas. You name it, if it robbed me of full night's sleep, it happened.
I would look for what is waking your daughter up at night. Is she teething? Does she have reflux pain? Are her feet cold? Is she getting too much stimulation right before bedtime? Is her bed comfortable? Sleeping on a hard crib mattress with a vinyl mattress cover is no fun for anyone.
There is a very specific time when "cry it out" works and in my opinion, it's never ever ever ever appropriate for an infant. When it works is when your 2 or 3 or 4 yr old is obviously having a stubborn tantrum. That's when you stand by and just let them cry and work it out.
With that said, I rarely took my kids out of bed when they woke at night unless they needed to nurse or were obviously in pain or made a mess of their bed. Leave the room dimly lit, dont talk alot or make a big fuss. I tended to what they needed be it a sippy cup with water, a round of teething tabs, a pillow under the crib mattress to elevate their head, checking for itchy wet diaper, cold feet, pajamas not pinching, etc. I would stroke their forehead to get them relaxed again and then say "time for night night" and leave the room. My kids would protest by crying a little and if they did, I just stroked their heads some more until they got drowsy and then left the room. I could always tell by the sound of their cry if I needed to go back - if it was that loud long sad wail, I went in. If it was that weak protest cry that settle down after 10 seconds, then I didnt.
I have 2 very strong-willed active boys and I never needed to let them cry it out as an infant to get them to sleep.
I hope that helps,
C.