Maybe it is better to also ask where she uses to be online more often.
Online right now : Cams.com, Chat49 and CamContacts
Yesterday : MyFreeCams
November 2 : Daily Peep
October 28 : Streamate
December 22, 2010 : Flirt 4 Free. She probably isn't working there anymore.
Over 1 year ago : Webcams.com
I don't know about the other sites.
Chat49 and Daily Peep are cheap sites, privates costing from $0.49 up to $0.99. It is common for models to not get naked on these two sites because the sites don't pay well. Mainly Chat49. On Daily Peep is a little different, but not much. Normally, on both sites, members end up watching a show the models are performing to members on another site.
Cams.com, I don't know what kind of private chat you want, but judging by the photos on her gallery, she seems to only do topless on Cams.com. Right now it is $1.99/min a private with her. But she seems to spend a lot of time in "nude chat".
MyFreeCams, $6/min, I have no idea if she is willing to do more than topless. But MyFreeCams may be the best place to have a chat with her before taking her in private. Use the PM - it is free - to ask about her private show. This way she will know what you want and you will know if she is willing to do so.
I hope this helps you.