AOA, thanks but I don't follow why "Aqeem-us-Salaat" should mean "establishing Allah's ordained government system". Do either of those words carry any meaning approximating "state" or "government"? As Sidqi bhai has mentioned, the Qur'an doesn't really specifically talk about states or governments, though it does mention office holders, whatever their power medium may be. Moreover, if we collectively aim for higher values, with or without any government involvement, we can all establish Salaat and Zakaat as social orders and via private organizations that further economic goals espoused in the Qur'an. And as for "equitable wealth distribution", higher callings at the individual level will have a far more profound effect towards this end than any government program. Employers can voluntarily choose to pay their employees more, we can choose to give back more to charities, start one, or take a more direct approach at the local level.
We will ultimately be judged as individuals, not as groups or nations; God won't judge our economic systems, but how we dealt the hand we were given. So as far as I can see, the highest goal of the sort of moral order we can hope for in a Kingdom of God would be to help develop, strengthen, and grow the average individual, not to infantilize them by looking to cater to their every need.
And I should emphasize that I've tried to be careful to speak of "average individuals" throughout. There will of course be exceptions, as there always are, in people who truly can't take care of themselves for any number of reasons; just as we wouldn't approve of leaving children on the street to fend for themselves.