Am I able to get a Masters in LIT and a PhD. in Rhetoric and Composition? Is this an okay idea as a future English professor?
Well, yes and no.
First, you should know that academic careers in the humanities (and especially in English literature) are ridiculously competitive. Most people who get a PhD in literature or a related field won’t become English professors. That doesn’t mean you shouldn’t do one; but it does mean you should be aware of this up front and plan for a potential Plan B.
Secondly…if you want to teach in an English department at most colleges and universities, a PhD in English literature will in general make you more competitive. If you look at the degrees that professors at most colleges and university departments of literature have, it’s usually in English literature. A PhD in rhetoric and composition will prepare you to teach writing and introductory to advanced composition classes, but not the literature courses that dominate most English departments. In theory, you’re only required to have 18 credits in literature to teach literature classes as a professor, which your MA in literature would provide; in practice, the field is so competitive that you may find it difficult to find a position as a university professor with the PhD in rhet/comp rather than lit.
I have heard from friends in the field that there is less competition for those writing positions, though, as fewer people get PhDs in rhet/comp than literature. The caveat is that the combo of the MA in literature and the PhD in rhet/comp may make you competitive for literature jobs - but you should ask professors in your English department. They will know.