Is it permissible to use Australian or imported sheep for Aqiqah and Udhiyah, given their dog-like appearance and the untried nature of their meat?

These lambs fall under the general category of livestock (bahimat al-an'am). The sacrifice (udhiyah (definition)) is permissible with any type of livestock (camels, cattle, and sheep), regardless of their origin, as Allah Almighty says: "And mention the name of Allah on known days over what He has provided for them of livestock." The same applies to the 'aqiqah (definition), provided that the required Sharia (definition) conditions are met.