I'm just here to tell you that you not alone! I'm in a somewhat similar situation as yours, except that I'm probably more messed up than you.
I'm also a local uni grad, second upper, engineering degree.
Took on my first job because the pay and leave were good. 2 weeks into my job, I knew I made a mistake to join this company because I hate most of the things I'm doing here. I know I'm going to leave this place eventually too.
I was in the same predicament as you, wondering how long I should stay before I look for another job. I'm now in my forth month. I thought things would get better, but they didn't.