What professional camera should I have for Fashion Photography?

Any Full Frame camera could be used Fashion Photography, the main thing is the lensing used in the shoots , Preferably all the block lenses  (Fixed Focal)  should be used as they give you a nice crisp contrast due to the quality of the optics is the best in block lenses.

I usually use my Nikon D90 Digital Camera 

personally am using Canon 5D MKIII but in general you can use any Full Frame Camera other different brands.

Presently i am using Nikon D750

Any camera is good, the lenses are more important, mid-telephoto and telephotos (85mm > 135mm) are preferred but you can use wide lenses too (35 and 50)

My advice will be that you go for Canon7D its the best in market nowdays and i have tried it myself also its awsome to work with plus canon has the the reputation for making user friendly product or you if you budget is low so you can go for Canon60D.
Although the main concern in photography is the lenses, so i would advice you5 lenes that you must have are mentioned below:
1- Prime Factor - Canon EF50mm f/1.4 USM Lens (Most important lens)
2- The Standard Zoom - Canon EF-S17-55mm f/2.8 IS USM
3- Canon Telephoto EF85mm f/1.8 USM Autofocus Lens
4- Alternative to the Super Telephoto: The Macro Prime - Canon EF100mm f/2.8L Macro IS USM5-24-70mm f/2.8L USM Zoom Lens (another ust lense to have) Hope this will help you.
Best of Luck!