Hmm, well they only need 1/46656th the food of a human so gathering isn't so bad. A single blueberry is a decent meal. Animals at this scale tend to spend proportionately less of their time having to gather food and more watching for predators, megafauna are the opposite, needing to constantly eat while having far fewer predators. This is also why megafauna tend to die out when there's a natural disaster like a longterm drought or famine, while smaller animals survive. Gnomes are probably going to deal better with things like the Toba supervolcano eruption just due to the advantages smaller animals have in times of famine.
They're going to have a catastrophic disadvantage when it comes to crossing water. Boats do not scale linearly, they become much, much more seaworthy, more efficient, and generally far better with size. Twenty-foot swells remain twenty-foot whether you're a gnome, a human, or a giant. The gnomes are simply not going to build anything capable of crossing the Atlantic until they're at modern-day technology levels. Possibly their biggest most advanced ships could, barely, survive the Mediterranean. Consequently they're unlikely to colonize the other continents until way further down the tech tree than humans did. Assuming they start in Africa like humans did, they can probably spread by foot to Europe and Asia but the Americas and Australia are out unless there's a convenient landbridge/icebridge.
On the flipside, they can fit people a lot more densely. A "Hide" (about 120 acres) was considered enough for one household in the Saxon days. With their 1/46656th the requirements that means a family will be able to survive in about a 10x10 feet plot of land (assuming equally productive land of course). Actually, I suspect they would do much better, because the trees and shrubs are relatively gigantic and thus their growing space is more three-dimensional than ours. Imagine how much fruit an apple tree a thousand feet tall might produce and you get the idea, a single berry bramble bush would be food for a whole village and provide shelter from predators as well.
As far as domesticated species, I could see rats as their replacement for pigs. Omnivorous, able to eat their garbage, sociable and domesticable, and once in a while they eat the farmer because they're also a very dangerous piece of livestock.
Rabbits are likely to be their "big game." A rabbit's instinct to run from absolutely everything will make them relatively safe to hunt despite the size difference, and the gnomes are small enough to go down rabbit burrows and flush them out in a pinch. When you consider how quickly rabbits are able to replace their numbers, the massive advantages the gnomes have at securing a food source becomes obvious. Due to their smaller size, gnomes are going to have more difficulty dealing with the cold and may well try to live underground in colder climes, possibly utilizing rabbit burrows. Burrows are also going to provide them with a superior defense against many major predators Rabbits may be entirely domesticable, and gnomes are likely to put far more effort into that than humans have, we pretty much just breed them for looks and don't worry about temperament much. If they can domesticate rabbits they might produce breeds entirely geared for digging burrows.
Various invertebrates are likely to not be domesticable as we use the term, but still farmable. Earthworms, f'rex, aren't going to be dangerous and are going to be delicious. Same with a number of grubs and other larvae. The gnomes may well stake out likely rotting logs to attract beetles and go in for a joyful harvest a few weeks before the grubs will pupate. Gnomes may put some effort into breeding a better and fatter earthworm, though the beetles may be much more problematic to successfully breed.
One thing of note is that their structures will not be scaled down human ones, f'rex the gnomes will not build an adorable fence two centimeters tall out of twigs. Anything small enough to be blocked by such a fence would be able to jump over it, gravity doesn't scale just as waves don't scale. The gnomes themselves will be able to take advantage of this as well, f'rex a gnome would be able to fall out of a tree twenty feet and land safely on the ground, and most of them should be able to jump several times their own height (This depends a bit on how ROB scales their biomechanics). Smaller buildings will also be much easier to build higher without gravity interfering. Consequently, gnomish architecture is going to tend towards several times more floors than ours does, and any walls will be dramatically out of scale for both height and thickness. Things like staircases are likely to be mostly ignored.
Megafauna won't really bother gnomes any unless they accidentally crush a home, which will, again, be avoided by burrowing. The main predators will be the same ones rodents have: snakes, birds, some of the bigger invertebrates, and other rodents. Burrows won't help with these but intelligently designed gates blocking burrow entrances will. Gnomish weaponry will be somewhat advantaged over ours due to scaling issues but a racer snake is still going to be a heck of a fight for them.
