You don't say how old you are, but on the assumption that you are thinking about this in terms of a university level training and then eventually a PhD and the university teaching career path (there are others – museums, archaeology), I would suggest you add to your current focus by looking at a couple of additional areas outside source texts (scarce) and secondary sources (really surprisingly rich). The first is to familiarise yourself with archaeology as a discipline, and with its contributions to Anglo-Saxon studies more specifically (these have been very substantial, to the point where archaeological work has been foundational over the past few decades to some major re-evaluations of Anglo-Saxon history). The second is languages: to be a professional in this field you would need, at a minimum, to be able to read Old English and Insular Latin, and probably to have some facility with the other major languages of the period, for instance Old Norse or medieval Welsh, as well.

The main training ground for Anglo-Saxonists here in the UK is the Faculty of Anglo-Saxon, Norse and Celtic at the University of Cambridge, and I'd recommend you take a look at its admissions site – not only to get a better feel for what is demanded of undergraduates there, but also to see what it teaches if you get there; note that the landing page includes a useful "Resources" tab that offers guidance on preparatory reading and a brief introduction to the languages. The good news is that they will teach you the languages from scratch.