Yeah, you can look for another job at any time. It doesn't put your current job in jeopardy. You can apply at as many places as you want and interview as often as you want; if they offer you a position and it's less appealing than your current job, you can always turn them down. If what you're offered is better, just put in your two weeks notice and tell the new place your availability will be open once that's up.
I did this recently. I got an offer from a clothing store that was quite a drive from my house, but since it was the first offer I'd had since I quit my previous job, I took it. I'd put in applications at a bunch of other places, but I didn't expect to hear from any of them until we hit peak hiring season.
I started at the new place and quickly found it wasn't a very good fit. The commute took so much gas money it turned the position into a minimum wage job, most of my coworkers were high schoolers with little to no work ethic, and I didn't like my manager. I'm not exactly a "fashion-oriented person" either. A couple of weeks after I started, I got a call from another place: a fabric store about twenty minutes from my house. I interviewed and got the job immediately. My manager at the clothing store told me she had no problem with me having a second job, as long as the fabric store worked around my schedule there. Problem? Well, in addition to the fact that I didn't really like the clothing store, they didn't release work schedules until three days ahead of time, and they only released them for one week at a time. The fabric store released schedules at least two weeks in advance and for a couple weeks at a time. And my clothing store manager was kind of a bitch about it when I told her that this was an issue.
Yes, the fabric store was for fewer hours, and paid less, but I liked it more. I put in my two weeks notice at the clothing place. The thing about the fabric store is that I know it's a hobby job, and I still need a full-time position somewhere to cover actual bills, get benefits, etc. But I don't want that full-time position to be a $9-an-hour job, 40 minutes from my house, that eats a quarter-tank of gas in the commute to and from every day. Even in the current economy, sticking with a job you hate when it doesn't have enough benefits to outweigh your dislike is a crummy long-term decision.
My previous job, the one I quit before? Didn't care for that one, but stuck with it for a year because it gave me management experience (good on applications) and offered medical. I quit to give myself real incentive to find something better, because otherwise I might've just stayed with it because it was "safe": I already had the job, and that's better than nothing, right? What I did was take a risk because I decided it was time to look for something more fulfilling. The place I'm currently working is the best job I've ever had even if I can't support myself with it. And the position I'm interviewing for now, the one that will be my full-time job if I get it, pays a lot more than anything else I've ever had, has more hours, and offers full medical, dental, and vision (the one I really need, that barely anyone else offers). Without the safety net of my old job, I'm a lot more inclined to look for real work.
I wouldn't recommend quitting first, though. Not the best decision I ever made. You can get lucky and find work right away, but don't count on it.
