A.P.
Hi V., I would recommend that you let her cry it out but do tend to her WITHOUT PICKING HER UP. If need be, sit by her side and talk to her to sooth her. This may not always work but it would be a step to reassure her that you are still there. I also recommend that you lay her or let her sleep with a pillowcase that you have used or a t-shirt- something that has your scent on it so she still feels close to you. I'm sure its scary for her to go thru this transition but you need to let her fuss it out and become acclamated to her new environment and sleeping situation.
If you decide to sit by her crib and talk to her, she will slowly get tired of fussing so much and you can gradually move further and further away from her crib so she acknowledges that she will be ok being on her own and that you are calm about it instead of you just walking away- then she'll really get scared if you act like you dont care.
I hope this makes sense and I wish you the best of luck with this.