There is nothing to stop you doing it on a private category or even permit aeroplane, except that if the instructor is paid there are maintenance limitations(i.e. within 62 days of a licenced engineer LAMS check). This is explained on an AIC.
Don't forget that you can revalidate as soon as you have the 12 hours including the instructor flight in the 2nd year, without losing any validity (i.e. for 2 years from the date of expiry of the previous SEP).
Better to do it early than risk going over and having to do a LPC.