(This answer will become invalid for trips commencing after LATAM leaves oneworld.)
Yes, but you have to purchase a particular fare that is not usually advertised (a oneworld global explorer fare, sometimes called a
xGLOBx fare, to be distinguished from the more usual oneworld explorer fare, an
xONEx). Any competent travel agent can arrange this for you, if you know what to ask.
No internet site is capable of pricing
xGLOBx fares, it has to be done by hand.
The specific fare will be an
LGLOB26 (economy), a
DGLOB26 (business) or an
AGLOB26 (first class, but none of the flights on your route offer first so this would be a waste).
Out of Sydney, an
LGLOB26 is presently priced at AUD 2799.00, plus fees, taxes and surcharges. The fees, taxes and surcharges depend on what countries you enter, which airports you land at and which carriers you fly on; but I would be surprised if they came to more than 1000 AUD. This fare permits up to 26,000 miles of travel, which should be sufficient for your purposes.
[Indeed, you have a further 4000 miles to use there, perhaps on your own domestic flights or in South Africa or South America.]
Round the world fares are issued by airline alliances. The difficulty you are experiencing is that the Santiago/SCL to Fa'a'ā/PPT route, via Easter Island/IPC, is operated exclusively by LATAM Chile (LA), a member of oneworld. Therefore you need to purchase a oneworld round-the-world fare. Yet, there are no oneworld carriers linking Fa'a'ā/PPT to Australasia. Air Tahiti Nui (TN), a non-aligned carrier, operates a service to Auckland/AKL from Fa'a'ā/PPT, and does so under a Qantas (QF) codeshare.
Oneworld issues several round-the-world and circle continent products. The one you see on rtw.oneworld.com displays the
xONEx product, the more popular oneworld round-the-world fare. However the oneworld explorer fare is restricted to oneworld carriers only.
The other oneworld fare family, the oneworld global explorer fare family, includes the following provision allowing travel on TN, provided it is under the Qantas (QF) codeshare (rule K in the Flight Applications category):
K/TRAVEL ON ANY AA/ AB/ AS/ AY/ BA/ BL/ CX/ EI/
FJ/ GK/ HG/ IB/ IG/ JJ/ JL/ JQ/ KA/ LA/ MH/ NU/
PG/ QF/ QR/ RJ/ S7/ UL/ WS/ XL/ 3K/ 4M
CODESHARE SERVICE OPERATED BY AA/ AB/ AS/ AY/
BA/ BL/ CX/ EI/ FJ/ GK/ HG/ IB/ IG/ JJ/ JL/
JQ/ KA/ LA/ MH/ NU/ PG/ QF/ QR/ RJ/ S7/ UL/ WS/
XL/ 3K/ 4M IS PERMITTED.
EXCEPTION - JL FLIGHTS OPERATED BY GK ARE NOT
ALL OTHER CODESHARE FLIGHTS ARE NOT PERMITTED
WITH THE EXCEPTION OF QF CODESHARE SERVICES
OPERATED BY AIR TAHITI NUI-TN
If your travel agent claims that TN is not permitted because of earlier provisions in the fare that appear to exclude it, please draw this paragraph to her attention.
[Note that the
xONEx fare family does not include this rule; its provisions are restricted to oneworld carriers and their affiliates:
J.TRAVEL ON ANY AA/AB/AY/BA/CX/HG/IB/JJ/JL/KA/LA/
MH/NU/QF/QR/RJ/S7/UL/XL/4M CODESHARE SERVICE
OPERATED BY AA/AB/AY/BA/CX/HG/IB/JJ/JL/KA/LA/MH/
NU/QF/QR/RJ/S7/UL/XL/4M IS PERMITTED. OTHER
CODESHARE SERVICES NOT PERMITTED WITH THE
EXCEPTION OF QF CODESHARE SERVICES OPERATED BY
JETSTAR /JQ /
ADDITIONALLY TRAVEL PERMITTED ON THE FOLLOWING
AIRLINES WHICH ARE AFFILIATED WITH/OR WETLEASE
PROVIDERS TO ONEWORLD