@MWolf of course you are right about music theory. The title of the thread indicates goals with music theory but the content of the first post by the OP mentions composition. Most composers I know end up teaching a lot of theory.
Apologies for getting off track for a person who might want to pursue music theory without composing. I made assumptions based on that first post and ignored the title, but the thread title may indeed point toward the OP’s desired focus.
Glad to be corrected and clarified 
I think @MWolf’s post may be helpful in showing the OP that these two areas of study should be seen as separate in terms of choice of a doctoral program. That decision is still pretty far off.
The PhD in composition involves a lot of writing, obviously, but the application involves submitting pieces and a personal statement, not research, in the places I know of. So pay attention to MWolf’s info.