You really shouldn't try to jump in the records from her birth to her death, without knowing anything specific inbetween. That's a recipe for genealogical disaster!
Since Jane Miles is such a common name, any Jane Miles that you find will be impossible to differentiate as "your" Jane Miles from other Jane Miles, without additional, specific information. Plus, her name could have been written Myles, Mills, etc. -- or even Jean, Janet, etc.
Alabama didn't have death certificates until 1908 so unfortunately there isn't a death certificate with her parents' names on it.
You should try to collect all the info you can in UK records first -- exact birth date, baptism (if applicable), etc. If you can't find her info then concentrate on her parents' and her siblings' info -- Did they all live in the same area? Did they get married in a church? (maybe she was married in that church) Where are they buried? (maybe she's there, too) Did anyone leave wills? (she could be mentioned in them -- or her children could be mentioned, if applicable.)
Are there digitized newspapers for the area? If she married or if she died in UK, she might be mentioned.
Have you searched any passenger or immigration records?
It's more likely that she died in the UK or that she married and remained in the UK than that she wound up in Alabama - especially since none of her family left. It especially doesn't fit that she married William Carmon in Tennessee -- because that seems to indicate that she travelled to Tennessee alone as a single woman.
Of course, it's not IMPOSSIBLE, but you need more specifics on her before you can make a credible "match."