Leash- Prior to retiring ( ) I used to work in this area and do these tests. The C-14 is absolutely fine to have done while BF'ing. To begin with it is the most miniscule amount of radiation that is used, so small that the test has to be sent off to be read by an ultra sensitive machine.
Point two, you ingest the C-14, unlike most nuclear medicine tests where it is injected directly into the blood stream. Sure a tiny bit may be absorbed, but you would get a higher radiation dose traveling on a plane.

I would more than happily have the test while BF'ing.

I don't think C-13 is available in Aus.

If you want more reassurance you could ring the place and ask to speak to a nuclear medicine technologist. We were always fielding calls about this kind of thing.