That will mean that your doctor thinks that you ovulated/conceived around Dec 30. That will mean that intercourse around Dec 26 to Dec 31 could have gotten you pregnant. At 12 weeks the scan can be off by as much as 5 days. That will move the latest date for baby making sex to Jan 6 and the earliest to Dec 21.
With your LMP date it however looks like the Dec 30 date is more or less correct. So Mr ONS on Jan 9 is very very unlikely to be the father of your baby.
Take care!