I have been asked to model so many times for big name cosmetic companies and clothing and I'm 5 ft lol but unfortunately I never took any of them so I don't think it matters much but in runway shows you have to be tall so that would def be out of the question for me lol or anyone in the height range but I think shorty have a chance in everything else ;)
I don't know about 5'1. 5'3 is already kind of pushing the minimum height limit for modeling. because it isn't like they can make you tall in 4inch stilleto's. Maybe catalog modeling but most likely not too much of runway.
If you have a decent look, do comercial print. Not clothing nessicarrly, more like tooth paste etc