If you want a prime example of satire, look no further. Swift is pretty keen on mocking the wealthy and their tendency to consume everything in sight. You might not get the joke for a page or so with the serious schtick, but A Modest Proposal is designed for the purpose of ridicule. Check out "Why Should I Care?" for more examples of modern-day satire.
It's not all a big joke, though. The idea of a world where we raise babies for slaughter is pretty horrific, and that's exactly the point. The dystopian genre often shows how an authoritarian or totalitarian government has gotten out of control, just like how Swift is pointing to the unchecked power of the landlords. He notes this when he talks about how his plan would help poor people "pay their landlords' rent, their corn and cattle being already seized, and money a thing unknown" (21).
A Modest Proposal is chock full of moral indignation—Swift's got a point to make, and he's not taking any prisoners. His bitter style of writing is classic Juvenalian satire, named after a dude who was angry about everything you could imagine. Juvenal, a Latin satirist in the 1st century CE, wrote about hating rich people, city living, and Roman society in general. And just like Juvenal, Swift's hatred is barely disguised:
I grant this food will be somewhat dear, and therefore very proper for landlords, who, as they have already devoured most of the parents, seem to have the best title to the children. (12)
Tell us how you really feel, Swift.