"This is someone who
enjoys belittling me in front of everyone"
SHE created the department. You suggested its creation BUT she created it. She holds ultimate responsibility for it to the organization, to the other employees and to herself. You just head it.
SHE is, therefore, going to judge your performance on HER terms using HER parameters and when you do not meet these terms or parameters, she is going to reprimand you on HER terms.
Should you ultimately fail, you will find yourself back in your old department as the best case scenario or out of a job in the worst case scenario.
To say that she
enjoys belittling you in public is therefore a sign of poor judgement on your part, in my opinion. SHE wants results and if "belittling you is public" is what gets results from you, she will belittle you in public.
So, my dear, stop whining and get down to business making that department out-perform all the other departments and then you will come back and tell us that you have been asked to form another department.
For the record, I have three lady superiors and when I mess up, take it from me, belittling in public is putting it very mildly what happens to me.