I think I definitely understand what you're going through, because I went through something similar when I was about to graduate from college (this was about 12 years ago, by the way).
First, to be honest, I dreaded graduation, because I didn't want to have to get a real job, leave all my friends behind and most likely break up with my boyfriend (he was going to grad school, and my job was halfway across the country). I was really genuinely happy in college and didn't want my life to change so much so quickly.
But, then it did. I started working in a new town, where I really didn't know anyone. For a while, a couple years actually, I had that really unsettled feeling. My job was giving me experience, but I wasn't all that happy. I made a couple of friends, but they were nothing like my friends from college or even high school. To top it all off, I was terribly worried that I'd never meet someone that I wanted to marry. Some of my friends got married right after college graduation, and I felt like I was "falling behind" everyone in the big scheme of life. Nothing seemed to be clicking.
All I can tell you is that after a few years, all of this passed. I did meet someone really great (my husband), and I'm pretty happy with my life. My job isn't perfect, but career isn't first and foremost with me, anyway. I never wanted to be a career-first person, and I think that was part of my anxiety at graduation. I felt like all I had to look forward to was a job -- and that wasn't what I really wanted from my life.
You are definitely not alone in your feelings. I think they're pretty common. And, the thing is, sometimes we look at other people and assume they have it all together because they're getting married or having kids or getting a great job. But sometimes those people feel just as "unsettled" as we do -- we just don't know it.
I think you're very normal. It makes sense to have unsettled feelings anytime you're about to move to a new stage in life.
Hope this helps,