Driving is easy in Croatia and this drive is pretty easy (I've never driven into downtown Split however) - but it may not be cheap for a one-way one day car rental. Price it out for yourself for this year - but maybe for September to get a good idea of long-term rates. (Try the Sixt website for example.)
One other option is a company I've seen (google for them, I haven't used them) that does a transfer from Zagreb to Split or vice versa, with a stop for a few hours at Plitvice. Might not cost less if any than just renting a car and doing it yourself but might be easier.
Be warned that crowds can get big in Plitvice by mid-morning - it's a very popular park, and it gets a lot of tour groups. You may encounter lines for boats and a lot of people on the boardwalks and trails. May might not be awful (I was there mid-May 2015 and it was not empty but not awful by noon). But if you can possibly swing it, overnighting at the park so you can enter the park as soon as it opens in the morning lets you explore it for a few hours before it gets too busy. At 7am it's still pretty empty and peaceful. FYI, if you did it this way, and stayed at one of the (overpriced but convenient) park hotels, you could do it by public bus. The latest public bus (last time I checked, who knows by next May) left Plitvice for Split relatively early in the afternoon, though. You can get the gist of the park in 6-7 hours though.