I had two papers published in Math.Comp. before getting my doctorate. (They were accepted before I even started my doctorate, but weren't published until my 1st or 2nd year at Oxford, due to the journal having a rather crazy backlog.)
If you can write well (i.e., understandably and in a style consistent with the journal) it's not a problem at all. Just write your paper and submit it.
Based on my experience reviewing papers (many of which are from non-PhDs) I'd say that the most frequent problem I see is papers which were obviously written without having any thought given to the journal to which it would be submitted. Go read a few dozen papers from the journal to which you're submitting, and get a sense of what topics are covered in the journal (this doesn't necessarily match the list of fields mentioned on the journal's website), how much knowledge is assumed of the readers, and how formal/informal the writing style is; then write accordingly. Bonus points for downloading the LaTeX style sheet and formatting your paper properly -- we can talk about how style shouldn't affect things all day long, but the simple fact is that having your paper look "different" will distract reviewers from what you're saying.
If you can write well (i.e., understandably and in a style consistent with the journal) it's not a problem at all. Just write your paper and submit it.
Based on my experience reviewing papers (many of which are from non-PhDs) I'd say that the most frequent problem I see is papers which were obviously written without having any thought given to the journal to which it would be submitted. Go read a few dozen papers from the journal to which you're submitting, and get a sense of what topics are covered in the journal (this doesn't necessarily match the list of fields mentioned on the journal's website), how much knowledge is assumed of the readers, and how formal/informal the writing style is; then write accordingly. Bonus points for downloading the LaTeX style sheet and formatting your paper properly -- we can talk about how style shouldn't affect things all day long, but the simple fact is that having your paper look "different" will distract reviewers from what you're saying.