The reason for QT your fish for 2 months is to let the display have no fish in it. Most parasites can't survive without a host so if you QT your fish and treat them, then they are usually not infected after about 2 weeks, but your tank can remain infected for longer while the parasites search for a new host so it is recommended when "resetting" a DT to keep it free from fish for two months or more.
Ich can survive QT if it stays in it's cyst form on the fish, there is no way to treat or get rid of it in this form, although the conditions of a QT are "stressful" enough then it can cause the Ich to prepare to leave the host, at which point it releases it's self from the cyst stage and would die in a treated QT.
A parasite by definition has a vested interest in co-existing with it's host. As long as no unusual disturbance takes place, it will continue it's idyllic existence , in harmony with it's host. However when a new specimen is introduced to the Aquarium, often the established inhabitants become quite excited, feeling that the newcomer will in some way, take their "space", eat their food, or even team up with their favorite fish/companion. This causes some form of chemical message to course its way through the fishes system, in much the same way, as adrenalin causes us, to become excited if we get a fright or suchlike. This chemical message, in some way alerts the parasite, which in effect says to itself, "Oh boy!, maybe I should get out from here, & look for a new host". The consequences are seen the next day, when it bores out from the host, leaving the telltale white spots.
To counteract this reaction, as much as possible, it is advised when introducing new fish to an established Aquarium, to do the following:
1) If possible quarantine the new specimen for 2 weeks. If the fish isn't eating or seems overly stressed you may need to make it shorter in order to save the fish, but you don't want to kill your other fish in an attempt to save the new one so digression is advised.
2) Introduce all specimens with the lighting as subdued as possible in the room, & with no lights on in the tank, continue this at least until the following day.
3) Change if possible one or two rocks, so that the existing fish are concentrating their attention on the change in the habitat they are used to, & not on the newcomer(s).