"Zij steunt me niet."
Translation:She does not support me.
I'm not sure which exercise you had, but "zij steunt mij niet" is also correct Dutch.
I had this as a listening exercise in which the voice did say "je" rather than "jij". Maybe the same for you? If it was a writing translation exercise though, of course your suggestion should also be correct.
Well, I had the Dutch-English translation exercise, and it said "Zij steunt ME niet." Look it up in the grammar rules.