Most companies, big or small, are not going to give their fresh out employees "interesting" work for the first six months or so. For one thing, you learned the requisite skills in college, but you did not learn the trade. Learning those essential skills takes a while. For another, your employer doesn't know up front whether you (or any other fresh out) can handle that "interesting" work. You have to prove your worth. Finally, your employer doesn't know whether they made a mistake in hiring you. There are a lot of fresh outs who should have majored in something other than what they did major in. Sometimes that mismatch only makes itself apparent after the new employee is on board.
Put all of those factors together and no, you will not get "interesting" work right out of college. Thinking you should is a false expectation.
Maybe, maybe not. Fresh outs often change jobs after a year or so. (That's the recommended length of time you should put up with a lousy job.) What certainly will look bad is if you have a string of those 9 month jobs. That's going to make you pretty much unemployable.
That said, you are not going to find a job tomorrow. Start looking now and you'll be lucky to find one in three months. By that time you will have a year with your current employer and you will be in line with other fresh outs who found their first job less than optimal.
This is assuming that your current employer will keep you employed. Unwritten rule #1 in finding a new job: Do so while you are currently employed. Do not violate this rule. Do not do things in your current job that will give cause for being laid off, or worse, being fired. Stay productive, stay interested. You might just find that your current job is a lot more interesting than you think it is now.
Take long lunches to "run some errands" and make up the lost time by working late, take three day weekends where those supposed vacation days are really for interviews. Your employer doesn't need to know what you do in your off-time. Your employer most likely does hire people away from other companies. They know the dance. Just don't charge your time searching as if you were working, and don't let the job search interfere with your current job.
That will set off some alarms, and it might even close some doors. A lot of employers check references *before* the first interview. Do you have a co-worker who (a) will say good things about you and (b) won't spill the beans to your employer?