My little sister very recently had surgery, where she had a cyst on her ovary and she ended up having to loose the entire ovary. So when I have mine out and gone, can they take one of mine, and give it to her?

I don't think so, but I honestly have no knowledge of the medicine surrounding this. 

<Jessica flipping through her Molecular Biology text>

Uh, give me a minute on this one. 

I think it's very hard to do, but I think there was a woman who was successfully transplanted an ovary from her mother or something, so if you are related it's easier of course... But yeah it might be expensive and it might be very hard to find an expert on that... But I'm not sure.

Found it! It is possible like Emily said with blood relatives. She would have to be on anti rejection meds for life and it may not produce viable eggs. It is also mucho expensive and is considered elective surgery since it's loss is not life threatening.

Yeah and it's risky to be on anti-rejection medication for that whole time, it would lower immune response to diseases and such... When I grow up I want to become a gynecologist and research/ballerina LOL u_u and I will found a way for us T-Girl and unlucky cis-women to be pregnant!!!

The anti-rejection meds are a pretty big deal. It's not likely to be recommended unless it's a pretty vital organ like a kidney, liver, or heart. It seems the downsides far outweigh the upsides in this case. If she's worried about hormonal levels, she's better off just supplementing the hormones rather than taking anti-rejection meds forever. Also, if it did somehow produce viable eggs, the kids would be genetically your children rather than hers. She'd be giving birth to her nieces and nephews.

Okay.
It's not that she was worried about hormones or anything, it was just that she was sad that she lost one, like this piece of her is gone forever, so I thought I could give her mine, and make her feel better.

It's the thought that counts. Give them to her pickled in a jar.