How long until you found a job? When/where to apply in Chicago?

I have just passed my NCLEX in PA and am in the process of transferring my license to Illinois, (I'm moving to Chicago late May). Now that all the paperwork is in place to do this I want to start to applying for jobs. Is it too soon as it is only late February?

Also, has anyone from the Chicago area recently been hired as a new graduate from nursing school? Or do you know which hospitals would be a good place to start looking for new grad employment? I have found a very few positions so far, most jobs need at least 1-2 yrs experience. My heart is in peds/NICU but I know I can not be picky right now.

It would also be nice to hear about how long it has taken people to find a job fresh out of school...a couple weeks, months, more? Any input would be appreciated, thanks!