Without knowledge of the climate of all countries you mentioned I guess it would be best to leave from UK late european summer. August/september or around there. You would by then avoid the intense heat of southern Europe and the Stans. Nepal is probably best in october/november and a little cold in december/january and ok again February to May and then the monsoon starts in June. I dont know exactly but I presume northern India had a similar climate.
Myanmar and Thailand will usually be at their best from november to february. March to May is usually ok too but can be very hot. June to september/october is rainy season for those countries. In southern Thailand it can rain until december.
Malaysia a bit similar but difference of west coast and east coast. Indonesia is mainly south of the equator and thus the picture is reversed a bit. The rainy season is usually from october/november to around april, although with big variations as it is a big country. Northern Australia should probably be avoided from november/december to february/march because of heavy rain and potentially flooded roads etc.

But 5-6 months is in my opinion to little time. You will have to race through the countries. I spent 3,5 months in Indonesia alone and I still regret I didnt spend more time there.
Shipping Dili to Darwin also takes at least 3 weeks and then add one week of cleaning and preparing and another week to get the bike through quarantene and customs clearance - it will be 5 weeks spend on that shipping alone.

Leave UK in August, spend August, September and half of October UK to India. Then India and Nepal October to december. Myanmar, Thailand and Malaysia December to January (not going to Laos, Cambodia?) Indonesia february and march, shipping Dili to Darwin one month, riding Australia a couple of months then another cleaning and shipping process - then your in NZ in July/August. I wouldnt do it any faster...and you would probably avoid the worst monsoon along the route except maybe from Indonesia.

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