When should I begin publishing?
My experience on this (Europe, physics department): I started my PhD last year, up to that point I had coauthorship on one publication (This dates back to my bachelors degree, I was a research assistant on a project that lead to a publication). Fellow PhDs in my current group have either one or no publicatiion as coauthors from their masters programme. 

To cut it short: In my field it would be quite uncommon to have your 'own' papers (as in first author, not sure if a journal would even accept such a submission) before you finished your masters, coauthorship depends on how keen the supervisor is on publishing results (and how well the overall research on that topic is progressing, my thesis was connected to a PhD's research, as those results could be published I got coauthorship).