Donald Trump, while publicly praising the latest sanctions, would certainly be aware of their limitations. If China had been serious about bringing North Korea to heel, it would have agreed to cut off its oil supply. It is also unclear whether China will fully enforce the agreed sanctions because it did not do so in the past. Russia appears bona fide in reining in North Korea but not China.
Trump may not have been entirely frank in his praise for recent sanctions. He had previously said (in a string of Twitter messages) that he was "very disappointed with China. Our foolish past leaders have allowed them to make hundreds of billions of dollars a year in trade, yet ... they do NOTHING for us with North Korea, just talk … We will no longer allow this to continue. China could easily solve this problem!".
China may have its own agenda in all this. It may consider a nuclear armed North Korea, its historic communist ally, to be in China's interest. A nuclear armed North Korea, would represent a major failure of US foreign and military policy, and would further weaken US influence. China wants to be the dominant military as well as economic power in East Asia and its surrounding seas, and has historic animosities towards the US and Japan.
North Korea itself has vowed to forge ahead with its nuclear and military programmes. In a statement from its mission to the UN it blamed the US for the sanctions and criticised the countries that had endorsed the resolution.
Given the likelihood that agreed sanctions won't work, there are several scenarios that may play out.
Trump can follow the example of earlier administrations and tolerate North Korea's continuation of its nuclear and missile programmes in the hope that they will never use such weapons. This would be at odds with his public statements but would reflect his current weakness in the context of US politics. There appears to be a much greater risk that North Korea would do something reckless with its nuclear weapons than is the case with existing members of the "nuclear club". North Korea, given another year or two to further develop its nuclear weaponry, will become a much greater threat to the US than it is now.
There is also the risk of proliferation. Abdul Qadeer Khan, the "father" of Pakistan's atomic bomb, reportedly confessed in 2004 to selling nuclear secrets. He tried to sell his secrets to Saddam Hussein, and did sell them to Libya and to Iran. China allegedly swapped rocket technology in exchange for Khan's secrets, and this has been incorporated into Pakistan's missiles. If this could happen in Pakistan, what is North Korea capable of? Would it be prepared to sell an actual nuclear bomb to IS, for example?
A second option is for Trump to place further pressure on China to cut off North Korea's oil supply by either threatening or imposing a trade war with China. This could cause China to relent out of self-interest, and would cripple North Korea economically within months, but this still might not stop Pyongyang's weapons programmes. If China did not relent and a US/China trade war eventuated, this would have major impacts on world trade, seriously weaken the Chinese economy, and would make China even less cooperative. It would also be very bad for Australia.
The third and most drastic option is military. President Trump now appears to be seriously considering such options.
Whatever Trump decides to do about North Korea and the growing reach of its missiles, time is running out. His main military option is a series of strategic military strikes, (I would guess) mainly involving the use of cruise missiles to take out North Korea's nuclear and missile capability. A full-on nuclear attack would involve less military risk to the US but (for ethical reasons) the US is unlikely to wish to be the first to launch nuclear missiles that would result in mass casualties.
North Korean Foreign Minister Ri Yong Ho threatens that, if the US attacks North Korea, the country "is ready to teach the US a severe lesson with its nuclear strategic force". Other countries were not being threatened unless they joined the US in a military attack. North Korea subsequently named Guam, the site of US military bases, as a specific target. It is widely speculated that South Korea (especially Seoul) and Japanese cites would represent soft and tempting targets, if North Korea contemplated a "doomsday scenario".
Trump has threatened to hit North Korea with 'fire and fury like the world has never seen' if it escalates its nuclear threat against the United States. "(They) best not make any more threats," he said.
In such a scenario Australia is looking very vulnerable.
Much of Australia may now be within range for North Korean missiles, and we have no existing missile interception capability. Our main saving grace is that Australia is a low priority and more distant target. We could become a more likely target as North Korea increases the size and range of its nuclear arsenal. The US could invoke the ANZUS Treaty in the event of conflict, but, given that any immediate conflict would mainly involve missiles and possibly US and South Korean military, there is not a lot that Australia might be asked to do in the short term.
Australia's main vulnerability lies in trade. We are highly vulnerable to either a trade war involving the US and China, or to disruptions caused by a military conflict in our export markets. Our four biggest two-way trading partners are (in order) China, Japan, the US and South Korea. If this dispute escalates, our trade with these countries could be severely disrupted, with potentially enormous negative impacts on our economy.