I can't vouch for the fairness of the scheme because I haven't read a critique on exactly how it would price and distribute energy in the real world. However, one has to begin with the presumption that the wealthy can buy as much fuel and carbon emissions as they would like, causing scarcity that both raises the price of fuel and reduces the amount of carbon emissions the less-than-wealthy can have. The scheme merely says that each adult is given an equal share of TEQs at the start of the year. If you use less than your share, you can sell your surplus; if you need more, you can buy more. Industry and Government bid for their units at a weekly Tender (auction). It appears that there are no limits on the amount of units that a wealthy person would be allowed to buy, although there is an annual "budget of units" that is projected until 2020. The story in the Energy Bulletin gives a bit more detail on the policy.
Even as a possibly flawed scheme, I would rather see one government move ahead and implement the policy as an experiment, to see how it actually plays out. We won't really know what the issues are until somebody tries it.
UPDATE: One question I had about the TEQ scheme was how energy and emissions would be counted in embodied forms: the purchase of consumer goods. TEQ has a scheme to count those energy and emissions units by requiring the producer to pay those TEQs. From The Oil Drum:
"The purchase of goods other than energy would not require the surrender of TEQs units, since the producers of those goods would have already surrendered units for the energy used in the production of the goods. Producers would then pass on the cost of buying these units to consumers, who would simply find that certain goods (those produced in a more energy-intensive manner) cost more."
However, this scheme hides the fact that a significant portion of goods in OECD countries (in some countries, the majority) are produced outside the country in places like China. The TEQ scheme, therefore, externalizes the energy and emissions costs associated with buying consumer goods to the country of production, where energy and emissions are not counted. This scheme gives consumers a free-pass to consume as much "cheap goods from China" as they can, since they will not have to surrender TEQs for those purchases. Furthermore, it gives a free ride to major retailers, like Walmart, who won't have to surrender TEQs for selling foreign-produced goods. It also penalizes the local production of goods, which may be producing such goods with lower energy and emissions and under stricter environmental laws. Consumer tendency would be to purchase foreign goods that don't reduce one's TEQs. This discourages the local production of consumer goods.