Lady,
Just hire a baby sitter for that particular day, she can come with you and the baby to the oath, which should take no more than 8 hours...
Remember that you can invite people to your oath ceremony, she can be your invitee, which will enable you to focus on the oath issues, be sworn in as a USC and enjoy the speech from Tom De Lay, he's the guest speaker in SFC on that oath day. Once the "festivas" is done, you go ahead and pick-up your child and both you and the baby sitter, husband head home. You pay the sitter and she goes home, both you and hubby, plus kids celebrate like it is December 31st, 1999.
Rescheduling might take longer, as BSmyth suggested, 3 months at time. If you or hubby is willing to wait that long, go ahead and knock yourself out. However, a baby sitter or grandma or pa watching your infant could help you out...