I think it seems fine, but, your miles compared to a direct routing are 50% more... (14.3k rather than 9.9k) - but with the stopover and as Australia is so far away I reckon it should be fine - even more so as the cook islands are hidden away! Obviously do the routing segment by segment via the ICC otherwise they'd say 'no'.

Suspect you might have more trouble lining up all of the flights - especially the cook islands, they might be popular on redemptions?

As an FYI, there are direct flights from MAN-SIN once a week, on Saturday (I didn't realise that until I checked staralliance.com looking at your routing - so don't know if you knew that). As its on a 772 there should be premium seats available too, so you might be able to avoid the MUC transfer (if you wished!).