620 to 750 in an 8-week timeframe is going to be pretty tough. Most people would need more time. Most people study for 3-4 months even when not going for a crazy-high score like 750 (by definition, only 2% of test takers get to that level!).
So, overall, I guess I'd say: go for it, but think now about what you want to do if you can't get that high in that timeframe. Would you rather lower your goal score but still apply this year? Or would you rather go for the score even if that means postponing until next year. (Think especially about the fact that you've already noticed that it's hard to get enough study time in... and you'll also need to be doing applications on top of that.)
Also, did you take that practice test under 100% official conditions, including essay and IR? If not, then your initial score may be artificially inflated. (Doing the initial two sections tires out your brain, which can affect your performance on the later sections.)
You say that you're "just starting a course" - do you mean an actual class? If so, do whatever the teacher / syllabus tells you to do. If you meant you were just starting out on a course of self study, then take a look here for how to develop your own study plan:
http://www.manhattangmat.com/blog/index ... an-part-1/Once you've figured out a plan for yourself, feel free to tell us about it and we'll tell you what we think. (Or, again, if you are in an actual course, then they should be telling you what to do! And you should be asking your teacher for advice about things like how to get the most out of your study time etc.)