Going through the list of things so far, to complete all of the quests you need to get:

x 2

x 3

x 3

x 2

x 3

x 3
This will give you enough of everything to make all the trade-ins, though with none of the trade-in items left over. That's 16 items in total, and I believe all of those come from the forest, so the quests could all be completed in 8 hours of searching. :3 That's not including finding pets and items in the forest though, so the actual time would be a bit longer.
As for the length of time between banners, the time is longer because the prizes are bigger - the 20 minute banners from the other Hunts only gave you a token that you usually needed at least a couple of to get anything, whereas this one can give you a pet right away. :3 Overall, the point is for it to take less actual hunting time to get the pets, since it's summer and a lot of people are busy with other things and wouldn't want to be stuck running to the computer every twenty minutes to look for a new banner. ;3 An hour gives people time to do other things and reduces the stress a bit.