He and his family moved to Tuam, in the mid-eighties before they emigrated to Mount Morgan, Queensland, Australia in 1988, when he was five years old.

In November he joined the Wallabies in France when fellow hooker Adam Freier sustained an injury.

After the whirlwind of 2005 where Moore made his debut for the Wallabies and featured in every Queensland Reds Super 12 game, 2006 was a mixed bag which saw him finish the season on the reserves bench.

However, his skills and strength as a ball runner brought an extra dimension to the Reds forwards and earned him selection on the Wallabies end of year tour to Europe.

[citation needed] In 2010, Moore appeared in all 13 matches for the Brumbies until breaking his jaw in the final round of regular season.

When Robbie Deans resigned following the Lions series and when Ewen McKenzie took over the reins, Moore started at Hooker for the Wallabies for the remainder of the 2013 Test schedule playing very well.

[6] On 6 July 2015, Moore was named as Wallabies' captain for the upcoming World Cup under new coach Michael Cheika.

Moore was made a Member of the Order of Australia (AM) in the 2019 Queen's Birthday Honours in recognition of his "significant service to rugby union, and to charitable organisations".