I just recently started watching the show and I saw an episode on Friday where Luanne had really short hair. When did her hair become short and when was she shown with longer hair again?

In the propane explosion at the Megalomart (the end of season 2), Luanne survived but all her hair was burnt off. The earliest episodes produced in season 3 have her hair short, to suggest that it's growing back. (But Fox ran the episodes out of production order, so in that season sometimes she has short hair, sometimes long.)