Is it focal length that's making my model look short?

I'm using Nikon D5100 and Fujifilm x100s to take some portraits or full length picture of a model. I use 18-105, 35mm and 50mm lens. Whenever I take a picture, my model legs are too short as they are in real. I also compared my image to one my friend's photoshoot, even though she is short and has a small body, her pictures look amazing with long lean legs and good body shots which filled the frame nicely. Is it because of the full frame camera or does it have to do with some editing magic?

Use that 50 mm lens to get the least distortion when shooting portraits. On your D5100, the 50 mm is a medium telephoto lens and it the best lens for shooting portraits. Backup from your model to get full length shots.

When you use wide angle lenses, peoples faces and bodies will appear distorted

It does not matter whether you are using a full frame sensor or a more common APS-C sensored camera, it is the lenses field of view that causes either near perfect portraits or distorted ones.

If you use your skills using the fundamentals of photography, use the correct lens focal length and do not shoot "down" on your subject, there will never be any need to retouch you images unless the makeup artist did not do their job.

You are more than likely shooting downwards at her. Place your camera at about her waist levl for a full length.

50mm lens!