Chart of the northern sky as seen from Australia on 9 November 2011, from astronomical twilight on. Ticks show the asteroids position at half hour intervals. Click to embiggen.
Asteroid 2005 YU55 zips past us in the next few days, coming as close as 0.85 of the Earth-Moon distances away. It will be closest to us on November 8, 23:39 UT, this translates out to around 10:30 am AEDST on the 9th in Australia.
However, while Australians miss out on the closest approach, from astronomical twilight on the 9th Australian observers will be able to see it scream along low above the northern horizon.
The speed of the asteroid, and the strong background light from the Moon make this an observational challenge. With strong Moonlight, you will need at least a 6" scope to be able to see the 11-12th magnitude asteroid (remember unaided eye visibility threshold is around magnitude 6 without moonlight, and in binoculars under moonlight you are pushing to go below magnitude 8, unless you have super tripod astronomical binoculars), and it moves so fast you will be able to see it move visibly against the background stars as you watch. Astrophotography will be particularly challenging.
The closeness of the asteroid means that it's orbital elements break most planetarium programs (eg. Stellarium puts the asteroid in completely the wrong position, and SkyMap is a little off). You will have to generate a topocentric ephemeris from the using the MPEC ephemeris generator, if you enter the latitude and longitude of your site, into the box in the ephemeris generator it will create a correct topocentric ephemeris for your site. My GRAS observing tips are here, and more observing tips here.
Despite the challenges, seeing this zippy little dot of light will be quite interesting, so why not have a go?