For that you would need something like «Vanno allo zoo dopo che mangio il pranzo.» or «Vanno allo zoo dopo aver pranzato.» ("They go to the zoo after having eaten lunch."). If you want to express that "I" is doing the eating of the lunch, you at least need a «che» between «dopo» and «pranzo».
Because, in this sentence, pranzo is a noun, not a verb. The sentence is not specifying anyone doing the action of eating lunch. If you want "They go to the zoo after they eat lunch," then you would need «Vanno allo zoo dopo che pranzano.» See my first comment on this thread.