Should a graduate student accept random offer to be a reviewer for IEEE Transactions paper?
It is probably a good thing to do, just for the experience. It will also get you on the good side of the professor.
However, make sure, in accepting, that the professor and others know that you haven't finished your degree yet. That might cause them to withdraw the invitation, of course, but it should be made clear.
Chances are the editor noticed you authored a paper on a similar topic and is inviting you based on that.
There's no harm doing this. You might feel you're not qualified, but you're being invited, therefore the editor thinks you're qualified. You shouldn't worry about writing a bad review either - full professors can write crappy reviews also, and if you read the paper in detail chances are you're already going to write a better-than-average review! If you're still concerned, you can always talk to your supervisor.
The fact that they addressed you as "Dr." doesn't mean anything. In situations like a reviewer invitation, where the editor is sending an email to someone they don't know well, it's common that they will address the email with some generic title like "Dr." or "Professor" even though the title may not actually apply to the recipient. It's just too much trouble for them to look up each person's qualifications and tailor the message accordingly. So I wouldn't consider that by itself to be cause for concern.
The fact that you haven't finished your degree is not a factor, in and of itself, and I don't feel it's necessary to inform the editor of this.
However, like any other reviewer, you need to make an honest judgment as to whether you have the necessary expertise to review the paper. Keep in mind that as a reviewer, the research community is counting on you to decide if this paper belongs in the scientific record in this journal. Some questions to ask:
Have you published in this area yourself?
Are you familiar with other work in this area, so that you would likely know if there are significant related papers that the authors have not cited?
Do you have a good sense of what most researchers in this field know, so that you can judge whether the article contains enough background information (or too much)?
Have you read enough papers in this field to have a clear sense of what makes a paper good or bad? What sorts of results does the community find interesting? What are common errors? What level of detail is expected? Which parts of the paper will need the most careful attention, and which are uncontroversial?
Have you read enough papers from this particular journal or conference to have a sense of the "quality" that they demand, or that their readers expect? Even if the paper is technically accurate and well-written, would you be able to judge if their results are significant enough to be worthy of publication in this particular journal / conference?
The average grad student is less likely to be able to answer "yes" to these, but you know your own background best. If you are not sure, you may wish to consult with your advisor or some other experienced research mentor.
It's true, as some other answerers mentioned, that the editor evidently thinks that you have the necessary expertise, probably based on your previous publication record or recommendations from other reviewers. But you still have to make the decision yourself, as you know yourself better than anyone else does. I don't mean to reinforce impostor syndrome here, but you can't say "the editor thinks I am qualified, therefore I am." I have certainly received papers to review where I knew I didn't know enough to do a good job, even if the editor thought I did. The editor is relying on you to evaluate your own qualifications, and to decline if you don't feel you can do the job properly.