You would indeed own the circle, if you were to buy the house, however I believe 'guardianship' may be a more accurate term.
I had a quick look at some of the Irish legislation and I found this:

National Monuments Amendment Act 1994
Section 12(3)
If an owner/occupier of a recorded monument "proposes to carry out, or to cause or permit the carrying out of any work at or in relation to such monument or place, he shall give notice in writing... and shall not except in the case of urgent necessity and with the consent of the Commissioners, commence the work for a period of two months after having given the notice."
Section 13
Contravention of the above subsection, among others, is here subject to the following penalties:
On summary conviction, a fine not exceeding £1000, or up to 12 months imprisonment, or both.
On conviction on indictment, a fine not exceeding £50000 or up to 5 years, or both.

Notwithstanding this, as you can imagine, the law is regularly ignored. So if you were to get your JCB to work, and it was a sufficiently secluded area and little known monument, you'd probably get away with it.

Seriously, as far as I know (depending again on the relative fame of the monument, and whether or not it is part of a complex, and indeed on the type of work you would be carrying out) the required buffer zone would vary. The absolute minimum would probably be in the order of 15 to 20 metres.

I should say that this is all information available on the internet, and from conversations I have had, so it's not gospel. Perhaps FourWinds has better or more up to date facts?