What do you mean by "update our filing status"? Update it where? Do you mean on the W-4 for withholding? You can update your W-4 at anytime, with the goal being having the withholding be similar to or more than your tax liability for the year with whatever filing status you will use on your tax return for the year. Give that you plan to file Married Filing Jointly for this year, your withholding should be made to match that. Given that you have been withholding for Married Filing Separately so far, you will almost certainly find yourself over-withheld when you do your tax return. But over-withholding is fine. Stopping the over-withholding for the last few months of the year is fine too.
(By the way, the only reason you would have to file separately before is if you were both nonresident aliens for tax purposes for the year, but people in J status, except students, are generally only nonresident aliens for the first 2 calendar years. e.g. if you came in 2022 or 2023, then you would be nonresident in 2023, but if you came on your J status any time in 2021 or before, then you would be a resident alien in 2023, and can file jointly.)
