It's going to be ages before they fully get one up and running but I think there has been some progress on this already right?
It's actually a lot closer than you think, I think currently they managed to make an operational quantum computer using 1000 qubits, called the D-Wave 2X System. You can check this out:
http://www.dwavesys.com/d-wave-two-system.
The challenge is that they need to be cooled to 0.015K, very near absolute zero for it to work properly. At this stage, there's a lot of development in building programs using qubits, and of course making the operation of such quantum computers more accessible to public

Ok...brain ~explosion~
What if, we were all relieved of our work duties, or at least to some extent, and then everyone's vocation became caring? So everyone works on becoming more caring for each other, but mainly the environment. They would call it: The Age of Compassion. Just as people see a duty to work for money, people would see a duty to work for the environment and each other. I know this is far fetched, but I'm actually really vibing with it? What do y'all think?
A really interesting way to look at it, when people no longer have to work for money to survive, maybe the world will be a better place where there will no longer be a cutthroat business world, where people compete with each other so much

Any ideas on where unskilled labour will shift to, considering that most of their jobs are becoming gradually automised?
The way I look at it, automation is very good at tackling 'maintenance jobs', which are jobs that are usually unskilled and repetitive, such as cleaning and cashiering. They are there to maintain the business operation, without adding anything new to the process.
On the other hand, for the 'innovative jobs'; actually automation may increase demand in this area, as humans are now more needed to think of new solutions; such as creating a new robot, implementing a new business model, finding ways to improve on existing systems, exploring the ethical and economical implications of automation, creating art etc. I'm not too sure if automation can perform such 'innovative jobs' by themselves, as robots and computers currently only act on human's commands.
This is why I think automation can be a good thing, as more people are freed up from 'maintenance jobs' to 'innovative jobs', increasing the rate of technological process and improving on the quality of life. However this also increase the demands on people to acquire more knowledge; which to some might be unappealing as they are required to do more study or they'll be left behind.
The saying "Knowledge is Power" is probably more relevant in the present and the future than before.