A number of issues with your proposal....
It could be done from southern South America with a radio transmitter pointed south and received from Australia
Due south would probably not be the best direction to point, but they are 5000 miles apart going that direction. That's a long way for bouncing radio signals...
If the transmission was picked up in Australia it would prove that the earth is round. If no signal is received it could prove that the earth is flat.
It likely wouldn't prove anything, but when you say it
would prove the earth is round and it
could prove the earth is flat, there is a subtle bias there. It might have be an error, but you should recognize any bias that could introduce errors in experimentation or conclusions....
It would need to be done during the southern hemisphere's summer, because of the greater range of radio transmissions.
A proper study should include any and all variables; summer/winter, hot/cold, day/night, etc....
There would also need to be a receiver north of the transmission to ensure that the signal is not headed in any other direction than south. Also, if the signal is picked up north from the transmission, it may be shown to be bouncing off of some sort of barrier.
Wait, so a signal received north of the transmission would mean that the signal was headed in other directions, besides south, but also could be going only south?? I hope you recognize the problem with that....
I know that no one can physically travel across Antarctica, but that doesn't mean that radio cannot be transmitted over the continent.
Yeah, as DNO said, people go all over Antarctica every year...
I'm not trying to discourage any experiments, but it's got a lot of holes, as is.