I believe it's the hair. 

Make sure that you are using the batch queue. It won't fix the problem but it can help get more frames to render before the error. If you are saving into a movie format instead of a sequenced images, that will also shorten the amount of time before memory error. Sequenced images help Carrara recycle memory. 

I had a project like that and simply had to divide up the render into segments, calculating and adjusting the frame numbering with the batch queue. No fun but it got the job done. 

This issue is not unique to Carrara and scenes with hair. Some other 3D programs handle hair more efficiently but hair is a memory drain to be sure. I just need a 2500 computer render farm...