I am myself a big fan of microlivestock, not the least because I am a pescetarian, and New Guinea has several potential candidates: Various
insects, such as: Giant stick insects (in OTL eaten in many parts of the island) - apparently quite easy to care for; and sago grubs (a delicacy among many of the island's peoples).
Nanolivestock! Very cool! Sago grubs have terrific potential. If you can get them to eat something other than palm pulp. The trouble is that if the Sago Grubs are dependent upon palm trees, then your nanolivestock has a bottleneck - it can take fifteen years for a palm tree to grow until it becomes fodder for a Sago Grub. This means that you're really dependent on a slow growing plant. Perhaps a related species of grub or beetle eating something else, or an adaptation or diverged domesticated form which eats other plant material like a prepared mash.
Giant stick insects, I don't know too much about. They seem to be social however, and leaf based plant eaters. So you've got possibilities.
Other potential livestock could include freshwater fish such as barramundi, eel-tailed catfish, croakers and gobies; a wide array of marine fish and shellfish, including groupers and the giant clam;
You need to be careful with those. The trouble with aquaculture is that your fish are going to be shitting and pissing (evacuating) in the same water that they're swimming in. In the wild, no big deal, population densities are low, there's a multitude of species, and a fully diverse ecology and running water cleansing the system. An aquaculture system, on the other hand, goes for heavy population density, controlled areas, minimization of species, etc. - quite often the result is eventually a toxic soup for your aquaculture. Modern Salmon Farms for instance have a variety of problems, including parasites, not seen in wild salmon.
Some species are tolerant, Asian Carp, or European Trout were raised by the elite in local ponds and pools just to have fresh fish around. But on the whole, it wasn't cost effective. As a general rule, you'd need pretty special circumstances for successful aquaculture. It's self limiting.
Some of the same things apply to nanolivestock. A lot of insects require a certain amount of space, they may not tolerate density, and they'll end up living in their waste product. The best bets for nanolivestock are usually colonial insects.
Dogs are highly virtual critters, and pound for pound, some of the most powerful draft animals out there. But they're also expensive to keep, unless you've got a ready source of protein, or edible forage - rough fish, meat or meat scraps, etc. etc. The Inuit and other Arctic cultures could use the dog as a draft animal because of the ready availability of sea protein, migratory meat, and low population density.
Eventually, silk worms, chickens, giant water bugs .
Silk worms are quite interesting. They're really the other great Nanolivestock. Are you thinking an autonomous route of domestication?
Giant Water Bugs? As I understand it, they're predators, which is usually a pretty black mark for a number of reasons. They're unlikely to tolerate being raised in density, and density is always an issue for any domesticate. In the wild, they're most likely prone to giving each other space - basically each to their own feeding/mating territory. Put a lot of predator insects in unnatural density, you may find them eating or damaging each other. Also, if they're used to low density, you may find that domestication densities will infect each other with diseases and parasites, resulting in the loss of whole crops. Finally, what are you going to feed them? From the sound of it, they're Apex insect predators, known to kill baby turtles and water snakes. So they're not cheap dates.
Interesting to see what you do with that.
and of course large domestic mammals, most likely water buffalo and pigs - at least at first, would become included in this livestock package
Water Buffalo domestication seems to date back about 5000 years, and emerges in India and China, spreading from there. Not sure when it would have made it into the Indonesian archipelago. However, we can assume that domesticated water buffalo are part of the package of an Austronesian agricultural complex. Your New Guinea civilization will encounter domesticated Water Buffalo late, on its extreme fringes, and as part of a rival culture.
Of course, they might domesticate it themselves - two independent water buffalo domestications make a third independent event quite plausible.
But then, the question is, where do you get your Water Buffalo? Odds seem remote that they might have gotten to New Guineau. The Anoa of Sulawesi seems to be a dwarf form of Water Buffalo, which indicates that some of them may have done some island hopping across the Wallace line during the glacial periods.
But a lot of my admittedly brief surveys suggest that the Post-Wallace Water Buffalo populations are either domesticates, or domesticates gone feral. Tough.
You can, of course, POD an introduction of Water Buffalo into Sahul, or New Guinea. As I've noted, Stegodons might be slightly more probable.
If you don't, then your New Guinea population has to expand outwards and westward into the Indonesian Islands, possibly as far as Borneo. And Domestication has to take place on outer fringes, and be imported.
As for pigs, not to sure about them, but I assume that there's a fair bit of literature about the proliferation of pigs and chickens. These seem to be part of the Austronesian package. I'm not sure if they proliferated in Indonesia before that before that.
Possibly an Austronesian Interchange is going to be a big part of your timeline.
Anyway, it would be fascinating to see a civilization or an agricultural complex working itself out with a large nanolivestock component, so I'm quite interested in seeing where you go with that.