The Full Moon is Sunday June 23 in Australia. At this time the Moon will be at perigee, when it is closest to the Earth. This is the closest perigee for 2013 at 356989 km. A full Moon at perigee has been called a "Super Moon", this is not an astronomical term, but an astrological one (see also here). While the Moon is close, it will have no real effect (or be distinguishable without a telescope and a good memory).
The Moon at Perigee and apogee as seen through a telescope. With the unaided eye, the Moon only appears half a finger-width wide, so the difference is much harder to see.
This months Full Moon could appear up to 14% bigger and 30% brighter in the sky than average. But will you actually notice if it is different to the last Full Moon?
The limit of distances that someone with good vision can distinguish between is 1 minute of arc (about the width of a human hair). So, for the vast majority of people any difference smaller than 1 minute of arc cannot be seen.
The Moon this Full Moon will be 33'57" wide (just a touch over half a degree, around half a finger-width wide), last months Full Moon (358374 km) was 33'47" wide. Without a telescope and careful astrophotography you will not notice the difference. For a list of full/new Moons and the dates of apogee/perigee see here.
If you can wait until January the 16th 2014, when the Full Moon is at Apogee, then it’s diameter will be 29'32" , and you could notice a difference if you have a good memory, but it won’t be spectacular. The illustration above is from November 28, 2012, when the Moon was at apogee and 29'33" wide when it was 406364 km from Earth.
However, while the "SuperMoon" will not be spectacular, it is still pretty and will be a good photo opportunity. If you have a decent zoom on your camera, after taking a photo of the Moon on June 23 and then again on January 16 2014 you will see a decent difference (you need to use exactly the same zoom enlargement, see Inconstant Moon for instructions).
And, no, we will not get earthquakes from the "Super Moon".