The regex (after you fix the non-escaped '/') will only check for the right number of digits.
It will not check if the month is between 1 and 12, the days between 1 and 31, or 30, or 28, or 29 depending on the month and leap years.
If that's enough for you, the closest you can get with regex is (assuming dd/mm/yyyy):
/(3[01]|[12][0-9]|0?[1-9])\/(1[012]|0?[1-9])\/([12][0-9]{3})/
Days will be in the range 1-31
Month will be in the range 1-12
I took the liberty to restrict the years from 1000 to 2999, but you can catch the format, if you want to restrict from 1970 to 2059 use (19[789][0-9]|20[0-5][0-9])
on the year part.
And you'll get the day on $1, the month on $2 and the year on $3 (I think)