I think you are more likely to get a job as a classroom primary teacher than as a piano teacher in a primary school - I have no idea what a Peri piano teacher is but am assuming that's peripatetic in which case I doubt there will be one with the govt. Primary positions in plum locations are hard to find at the best of times so you may have to be prepared to go to perhaps more out of the way places. Your piano skills will give you an added string to your bow when you apply for positions though. You may have more luck with the private sector as they are more likely to have the added extras in their curriculum and have the parents to pay for them.
Good luck with your decision whether to bring your piano or not - guess it all depends on whether you find a house big enough to accommodate it as well.
You could start looking at the links here
Careers & vacancies home page for jobs.