Have you tested yet? If not there is really nothing the Recruiter can do except look at jobs based off your practice test score. If you have tested and it's not showing up on the system for your recruiter then it's probably not available.
Look at it this way, right now the Army is going through a down sizing, jobs aren't going to be just given out to whoever wants one like they may have been during the surges. You may get lucky and get MP but I'm almost 100% sure you won't get dog handler right out the door, if you get MP get to your unit and find out how to get to the school.
Your ship date will be based off each job so it will be different for every job that is available to you. Right now, where I'm at, most are waiting a minimum of 3 months to ship out. That's just the way it is right now. On rare occasions we have gotten people out of here with a month or so.
How badly do you want in the Army?