Under the FAA system, you don't need a type rating (endorsement for we out-of-step Aussies) if its max AUW is below 5700 kg. But you would need an instrument rating, multi rating etc as applicable to the operation to log time.
For anyone brave enough to ferry a single, I suppose you could log the time as either x-country dual or ICUS, but it would have to be under the auspices of a recognised flying training organisation, controlled somehow by a CFI. I don't think a student pilot can just jump into any old ferry situation with a non-instructor in a non flight school operation and log the time.
On the other hand, an unrestricted PPL could probably log the whole lot as command, or ICUS depending on the mood of the ferry pilot. Who could challenge it?
If the aeroplane is tanked for an overweight ferry, not many light twins or singles would be able to carry two pilots anyway. Sounds a bit suss to me, so don't send money!