I read medieval Latin fairly fluently, and more precisely the very formulaic Latin of Carolingian chroniclers and biographers. I can typically get the gist of a brief passage without consulting a dictionary, and I'll look up particular words as needed. Anglo-Saxon Latin is happily similar, with the notorious exception of Aldhelm, whose sentences go on and on like Texas. Niermeyer, Whitaker, and Perseus are my friends, and I often consult an app called 'SPQR' on my phone.

Conversely, I struggle with legal documents from the same period, and near-contemporary Visigothic or Merovingian Latin is Greek to me. Medieval poetry is impenetrable. The shorthand used in earlier Roman inscriptions is Morse code, and I can only trudge through the syntax of classical texts like Cicero or even Augustine with an English translation in hand. Late medieval Latin is a brave new world of vocabulary and syntax, which I can sometimes navigate by parsing grammar and looking for modern cognates.

As a historian of the early middle ages and (I flatter myself) late antiquity, I'd say my Latin is somewhat above par. My peers and colleagues are by and large just as competent in the language, but I think I feel a bit more comfortable than most. That said, classicists and undergrad classicists who cross over to become grad or post-grad late antiquarians have a grasp of Latin which I simply cannot rival, and they're able to precisely identify what every word is doing in isolaton when I rely on context to help me out. For certain lines of research, this is not an advantage but a necessity.

I've taken the liberty of responding as a medievalist because, at least in American academia, there are very few scholars studying the classical period within history departments. Roman historians more often dwell in the ever-dwindling classics departments, where the task of knowing Latin—and also classical Greek—supersedes possessing the skills of a historian. In short, without a thorough undergraduate education in both Latin and Greek, it will be an uphill battle working to become a Roman historian within the US university system.

As a point of reference, you might be interested in looking at the requirements for the ancient history and classics major at OSU or the requirements for acceptance into an ancient history graduate degree there. OSU is one of the few US universities I know of with exceptional strengths in both classics and ancient history, although that's certainly not to say there aren't other programs I don't know about.