It can take anywhere from a month to several months, depending on the plan administrator's cooperation in pre-approving the form of order, and the time it takes for the judge to sign the order. I recommend using a QDRO attorney to facilitate the process.
Please note that I am answering this question as a service through Avvo but not as your attorney and no attorney-client relationship is established by this posting. An attorney-client relationship can only be established through signing a Fee Agreement and paying the necessary advanced fees.
If the plan administrator pre-approved the QDRO, 30-45 days should be enough. Find out when it was signed by the judge and a certified copy sent to the plan administrator. Then call and ask about 3-4 was after it was sent.
I am not intending this to be legal advice, because I don't know the particulars of your situation. Call me if you would like to discuss this or other isues.
Under ERISA the retirement plan has up to 180 days to qualify the DRO or reject it. If the DRO is not qualified you will have to draft a new one with appropriate language, have it signed by the judge and resubmit it to the plan. The processing timeframe depends in part on how fast the plan administrator (or outside legal counsel) normally processes those orders and partially it depends on how closely the DRO language tracks plan language. If you used some form you found on the internet or had an attorney draft a very specific and unique order then it will take the administrator far longer to determine whether the DRO language meets the plan's requirements.
Once the DRO has been qualified, the plan has a reasonable amount of time to process the segregation and notify you that the segregation is complete. Once the segregation is complete your ability to obtain the assets available to you as an alternate payee depends upon the type of plan, the plan rules and what the QDRO has ordered. For 401k plans the assets are usually available in full right away but if this is a defined benefit pension plan you may not be able to obtain a distribution immediately and/or you may be required to accept payment on a monthly basis rather than a lump sum distribution.