It's not the agreeing to file divorce, it's agreeing to all the terms of the divorce. If you have a complete (written) agreement on all issues, the minimum time is six months from the date of service of the Petition.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
It sounds like while you both agree to the divorce itself, you may need child support and custody orders at a minimum. If you both agree to the terms for child support and custody, then you can hire an attorney to draft the Stipulated Judgment and the process for finalizing your divorce should be pretty easy. If he doesn't want to pay child support, for example, then you will need to litigate the case and file a Request for Order seeking child support. I am including links below describing the divorce process as well as how you would go about seeking a child support order. Good luck.
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