If the LFS has already cured the rock and you take it home in the manner you mentioned then you will not need to recure it, but you will also be OK with the wet newspaper route since your drive is not very far.
As far as your QT tank, a critical question needs to first be addressed. If your fish develop ick or any other sickness, will this QT also serve as a hopital tank?? Will you add medication to your QT?? If so then NO live rock nor substrate should be added. You stay ontop of your parameters with many water changes and only buying one or two fish at a time. If you will not medicate this tank and it is solely a QT, then you can add as much LR or LS as you want. It would not be wise to plan on adding it to your display since your fish MAY come down with a parasite. And some parasites, even ick can be transported through the water and your LR may transport it into your display.
But, while having three tanks would be a perfect scenario (display, QT and hospital) it is highly unlikely than an aquarist would have the recources available to achieve it, so in short, keep yout QT bare
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The absolute safest time period to QT a fish is 6 weeks.
But some feel confident after 2 or 4, it just depends on how cautious you are.
It may also help to know how long the fish was at the LFS, if tankmates were infected, if fish in other tanks were infected and if they all share the same filtration system.
I had bought a dwarf angel, and the LFS owner told me he had had the fish for about a month, so I only QT'ed him for 2 weeks, but if he had just gotten him in, I woulda been a little more cautious.
HTH's