Folk Etymology:

A folk etymology is a change in the commonly accepted origin of a word or phrase resulting from the replacement of an unfamiliar form by a more familiar one. The form or the meaning of an archaic, foreign, or otherwise unfamiliar word is reinterpreted as resembling more familiar words or morphemes.

I encourage you to consider the difference between these two phrases or terms:

1. "related to"
versus:
2. "originated from"

In the minds of many signers the sign AUSTRALIA is indeed currently "related to" or "associated with" kangaroos. That is what they think of when they "relate to" the sign AUSTRALIA.   Let me state that again.  Many people really do make the association between kangaroos and AUSTRALIA.   If the sign for AUSTRALIA started out being associated with something else that doesn't mean that AUSTRALIA isn't currently influenced by the mental association many people have today.

Once in a while two ideas get romantic, then pregnant, and something NEW is born. Here are the two ideas:

1. British prisoners being picked up and dropped off.
2. Kangaroos bouncing along

When we take the handshape of the "pick up and drop off version" of the old sideways moving sign for AUSTRALIA and combine it with the forward moving bounce of a kangaroo -- Shazam!!! -- A new baby idea (or association in the mind) is born -- and that idea now has characteristics of BOTH its parents:

The

A defensible statement regarding the rationale and/or etymology for the (current as of 2019) sign for AUSTRALIA might be: 

The handshape, internal movement (8-handshape changing to an open-8) and arching movement of the sign AUSTRALIA probably originated from the concept of British prisoners being exiled (picked up and dropped off) to Australia.  The direction of the sign (forward, rather than sideways) and ongoing apparent evolution in handshape (as documented in occurrences of handshape variations depicting paws as seen done by some Portuguese and Turkish signers) are indicative of an association with the sign for KANGAROO.

Here is an example of the "pick up and drop off" version of AUSTRALIA as done by Karl O'Keeffe, webmaster of http://www.signmonkey.net/ --- an online video dictionary of British Sign Language.

(Source: O'Keeffe, Karl, (n.d.) "Australia," Signmoney.net, Retrieved 1/19/2019 from: https://media.signbsl.com/videos/bsl/signmonkey/mp4/australia.mp4 )

Just because a sign has "one" origin story doesn't mean that the sign cannot continue evolving, change into a new sign, and be associated with a new or different "origin" or "reason for being signed that way." It is quite likely that people worldwide associate Australia (the place) more with kangaroos than prisoners. The question becomes:  Which do more people associate with Australia?: Prisoners or kangaroos?  Imagine this:
Signer 1:  Hey, I have an idea!   Let's do a sideways pick up and set down movement and associate it with "prisoners."
Signer 2:  Hey, I have a better idea!  Let's take that sign of yours and move it forward instead of sideways and associate it with "kangaroos!"
Signer 1:  On no!  It was my idea first!  You can't modify or change my idea! 
Signer 2:  Opps, did it. 

Eventually even more than the movement direction of AUSTRALIA might evolve.  For example, here is a version of AUSTRALIA as being done by a signer using Portuguese sign at the Spread The Sign online dictionary:


 

Here is a version of AUSTRALIA as being done by a signer using Turkish sign at the Spread The Sign online dictionary:

The above are examples of AUSTRALIA. They are listed under the "Australia" entry for their respective signed languages. These examples are included here to help demonstrate the fact that some signers or signed languages have evolved further away from an association with "pick up and drop off" and closer to an association with "paws and hop, hop."  The versions above also are representative of how many people sign "kangaroo."  Thus we see the sign KANGAROO being used by some people to mean "Australia."

Notes: