No, you don't. There is no such "6'months rule". Use your judgement and do what is best for you.
I don't recommend that you leave your present employer. See if things can still work out. If not, just tender your resignation. There is no bright "time line".
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
Law Offices of J Thomas Smith J.D., Ph.D 11500 Northwest Freeway, Suite 280 Houston, TX 77092 713-LAWYER-2 www.MyImmigrationLawyer.info NOTE: Responses are for the education of the community at large and is not intended to be "legal advice." No attorney-client relationship is established by responses or comments.
Talk to an immigration attorney. Too many variables to address this question on AVVO.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
Once you have your greencard you are free to do as you please.
Consult with an experienced immigration attorney or make an info pass at your local USCIS when you need advise. Street law is rumor and "advise" you receive is based on someone elses case which may have nothing to do with yours. I consult with many persons on a regular basis who end up in deportation proceedings because they listened to street advise rather then consulting someone who knows.