Is this a good idea
No. Shopping around the different ROs undermines the work your recruiter has already done. Plus, you didn't fully qualify until November. It's been 2 months, most people wait anywhere from 6 months to a year or a ship date sometimes longer.
Follow up with your recruiter, but be POLITE and PROFESSIONAL with them. It's likely your recruiter is working a few dozen cases, plus collateral duties.