Whether you're after graphic design jobs or illustration, you need to know what the going standard is. Take a hard, objective look at your work before you start looking for jobs. Is it up to the standards of most of the work being published? You need to meet or beat the quality level you see at the company you'd like to work for in order to get hired.
If you don't think you can be an objective judge, talk to a professional who's had some design jobs, or go online to some of the forums where the pros hang out. Be ready for possible harsh critique, however. Graphic design jobs and illustration positions aren't for the faint of heart or easily discouraged. You're going to be in competition against people who have a lot more experience and better skills than you do. Only hard work can bring you up to par.
Now, think about how much you want to work on art every day. After all, what's fun from time to time can get pretty dull if you have to do it eight to twelve hours a day (not uncommon for freelancers) every day of the work week. Think about your ability to deliver on time and how well you can communicate with clients. If you're at the mercy of your muse and haven't learned to make art in any mood, design jobs might not be the right choice for you right now.
Do you want to work full time or part time? Most of us would reply full time at first, but it's important to think past that reaction. After all, there aren't too many steady art positions with full benefits out there. Many artists and graphic designers are freelancers. That means that their workload tends to be feast or famine, and that they don't have guaranteed health insurance, retirement benefits, or many of the other things that might come with a more conventional job. Because of this, many artists work a more normal job on the side.
Do all these things mean you shouldn't become a career artist? Of course not! Just make sure you know what to expect and are actually ready to jump in. If you still need a little work, try doing some low profile jobs for less pay or on a volunteer basis. You'll end up honing your skills and get a good taste of what it's like to do art for pay, without committing yourself too much. Take some time to talk to professionals, too, and put together the best portfolio you can. The end result is worth it.