You said you were visiting Caxias do Sul and you have 3 weeks. So the first question you have to ask yourself is how long you plan to be in C. do S. When you ask about the "one spot which a birder should visit", are you talking about Rio G. do Sul or Brazil as a whole? If the latter, it is a much more difficult question. My answer would be south east Brazil (Sao Paulo, Rio de Janeiro and Espirito Santo states) given the number of endemic species in this area. Some of those, as well as a large number of Atlantic forest species, can be seen in places much closer to Caxias do Sul though.
Regarding the Pantanal, which is a very large area, the bulk of the rains fall between November and March. The Northern Pantanal, the area that is reached by flying to Cuiabá, floods first and should be getting quite wet by December. In fact many, but certainly not all, of the lodges in that region close between December and February. The Southern Pantanal, the area reached from Campo Grande in Mato Grosso do Sul state floods later. In fact when the flood reaches its peak in the south the Northern Pantanal is in the beginning of its dry season. However in December all of it is bound to be very hot and very humid with lots of biting insects. Also the frequent rains can make the unpaved roads in the best wildlife areas not passable by common cars. Thus it is probably not the best time to go but I have no direct experience at that time of the year. The overwhelming majority of the birders visit during the dry season.
If you must be in Caxias do Sul for sometime and plan to rent a car, I would make the following suggestion: read the write-ups for Rio Grande do Sul, Santa Catarina and Paraná states in the web site quoted by Guy Kirwan in one of the above posts (
http://ricksimpson.wordpress.com/jeremy-minns-site-notes/ ). For example, with a rental car, from Caxias do Sul you go to Sao Francisco de Paula, Cambara do Sul e Aparados da Serra NP, birding along the way whenever possible. Then south to Lagoa dos Peixes. This would take a week at least. Then back to Porto Alegre and fly to Curitiba, rent a car in Curitiba and visit sites between Curitiba in Paraná and Joinville in Santa Catarina. Then fly to Foz do Iguaçu, do what you want to do there, remember that is easier to bird in the Argentinian Iguazu National Park than in the Brazilian side. This could take another week at least. After that fly to wherever your international flight departs. You can save a lot of money on the flights by purchasing a Brazil Air Pass, has to be purchased in your home country, can't be purchased in Brazil. A cheaper but more time consuming option would be: take interstate bus service to Curitiba, rent a car in Curitiba as mentioned above, then take bus from Curitiba to Foz, then retrace your steps. You could also do a big driving loop: Caxias to Aparados area from there to the Joinville area and then back to Lagoa dos Peixes then back to Porto Alegre and then fly(or take the buses) to Foz and from there fly to wherever your international flight departs. One, seemingly logical option, turns out to be extremely expensive: renting a car in P. A. or Caxias and returning it in Curitiba. As far as I know this is possible but the rental agencies charge an enormous fee, basically you pay the expenses for one employee to go get the car and drive it back to the rental agency where you rented it!