First of all, just because your husband will owe taxes (because of no withholding) doesn't mean he "can't" claim his child as a dependent. He certainly can, if that's what you want to do.
Second, you will probably pay lower taxes overall if you file jointly, especially if you have a child. Many deductions and credits are limited or disallowed for married filing separately. If you wanted to file jointly, then you do nothing now. Wait for your original tax return to be processed and your refund paid. Then, file an amended return to change to married filing jointly, and add your child and your spouse's income and deductions.
Finally, if you still want to file separately, then your spouse can file a separate return at any time. You will need to wait for your original refund to be paid, then you can file an amended return, keeping as married filing separately, but adding your child.
In all cases, the amending software won't be ready until some time in March.
*Answers are correct to the best of my ability at the time of posting but do not constitute legal or tax advice.*
