If the Tardis is in the time vortex, there isn't a real date of birth.
So I guess they would go with the date on the planet of origin of the parents the next time they visit it (minus the time they spend inside the Tardis since the birth).
Well I guess if you are on a planet you would take the date not the year. Then you just gauge time spent on the TARDIS. I would think that no matter where you jump to or where you go in time that a day is a day and a year is a year. If born IN the TARDIS...Well They have ways to find out the date. So ...What if they are born ON the TARDIS...Well now my brain is broke so I can not go on trying to answer!!!