Firstly I would say don't worry, just go ahead. Babies are resilient and can cope with a lot. E.g. if it's not too hot for you, your baby can handle it too, with a little care. Traveling with small kids (with a bit of thinking ahead) will leave you with incredible memories (even if they don't remember a thing)

With our infant son, and more recently our infant daughter, we have visited many luxury hotels, including many Amans and Four Seasons, safari in South Africa, several New Zealand lodges (Farm at Cape Kidnappers, Kauri Cliffs, Wharekauhau), and numerous others across Asia and elsewhere (eg Trisara, Song Saa, Chedi Muscat etc) and in cities around the world. I can honestly say we have never had a really bad child experience.

Aman in particular are fantastic with children and have often gone out of their way to babyproof rooms and provide whatever we may need. Babysitting at Amans (particularly in Asia) is cheap and very high quality, which is a huge plus. As mentioned above we have also found Four Seasons to be great.

Yes you do need to work around naps and other baby requirements but to be honest there isn't much you can't do on the go (babies can be fed/diapered/napped pretty much anywhere... and they don't really get jetlag until they are older)

I strongly agree with the above point that suites are important for allowing you to put baby to sleep and still enjoy your naptimes/evenings.

To your questions -
- In general with a kid up to about 2, just pick where you want to go and go for it. They won't remember anyway and everything is interesting to them; you don't need particular kid activities until they are older.
-Amanzoe with a 4-5 month old would be great; he won't be able to move so no worries on the pool. and even when they can crawl/walk, unless you completely ignore them you can avoid them falling in pools. For the heat, just get a fan to clip on the stroller/car seat/sun lounger and keep them in the shade (we did the Middle East in September with our 8-week old; it was pretty toasty but she didn't seem bothered)
-Maybe consider swapping your Asia/Australasia trip with the Sept/Oct one? We found that around 9 months, long flights got a bit more challenging as they are old enough to get bored and move around but not old enough for an ipad to entertain them (that started working around 20 months for us). That said we still managed many long hauls in that window (including many on my own with kid/s) and survived, just not exactly fun

Just do it. before you know it you'll have to worry about school holidays and multiple hotel rooms and kids club facilities and whatever else. With infants it's a breeze