Non-motorcycle -- converter for 60Hz power ?

idk said:

I suspect that the power may have to be converted to DC and then back to AC in order to change the frequency....

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Well that is one possibility but 'clunky'

If that were case what you would be looking for would be a US spec 12V DC to 120V/60 Hz Inverter to take with them and then just buy a 12V DC Power Supply in Oz.
Both will need to be rated for at least 1200W (and bigger might be good insurance)
The biggest problem there is not so much the inverter but the 12V supply - that needs to be capable of 100A at 12V to supply 1200W

So a turnkey solution is probably more practical - none of these are likely to be inexpensive - here are a few I found in a quick Google search

Single Phase 60Hz to 50Hz Converter

Frequency Conversion: AC Power Converter – Three Phase & Single Phase (2kVA model)

Solid State Frequency Converter Specifications 1.25kVa


Check to see if they really need the full 10A - a 1kVA may suffice but might have to go higher (2kVA) if really want the full 10A capability (1kVA is going to be a bit less than 10A - 2kVA is going to have a lot of overhead)
I suspect this may be for a medical application so like everything else 'bigger' is going to have more overhead and be less taxed at any given current.

Also, 10 amps at 110 volts is about the same as 5 amps at 240, if my old memory serves me correctly.

Yes, but that is only on the input AC supply (and not accounting for any losses in the power supply - cooling fans etc will also add to that) and simply a straight transformer ratio if this was a simple step-down (same frequency) unit.
If using the two separate modules (i.e. AC to DC & DC to AC, the DC supply, regardless of only pulling 5A from the wall for just a raw ratio (and it would be higher than that in real World), it still needs to put out 100A at the 12V output to put 1200W in;
And for the AC to AC unit (Step-down AND 50 to 60 Hz), regardless of the input current at 240V (and there will be some losses in the power supply itself) it still needs to be rated at 1.2kVA for the output power and the input will be whatever it needs to be to supply that plus any overhead current used by the unit.
So I wouldn't even look at the input current requirement at 240V - in either case, the output current is the spec to look at and any module that is capable of supplying what is needed at the input will present no problems to the input side, or the wall socket.