It doesn't matter which way around you connect the wires. It will work
either way.
BTW FYI the brown wire is actually active, NOT earth. Since you made this
mistake, it sounds like it's best for a qualified person to do the
connection, or at least check it before you use it.
Also, as there seems only to be two wires coming from the plug, I am
assuming the plug is a moulded type with only two pins. If so, and if the
heater element is still connected, be careful about the rating of the cable.
Many heaters use the full 10 amps (Australia) of a power point. A "normal"
two pin plug with only two wires is usually rated at only 7.5 Amps.
Cheers,
Phil