Can you please tell me if it's my fault my girlfriend has an eating disorder?

Not your fault: Why would you think your girlfriend's illness is your fault? You can encourage her to get help for this problem, but it is her business. If by chance you're over-focusing on her weight, or comparing her to other attractive, thinner women, you can stop that. Hopefully she's not trying to starve herself to be attractive to you, as no romantic partner is worth sacrificing one's health.