There's certainly no need to dress up (though you're very welcome to and
some people now make it a point to dress up a little whackily for the Festival).
But most people simply wear
whatever feels comfortable.
If you're planning on a full day of fun, though, it's probably wise to slop
on a bit of sunscreen and bring along a hat.
A lot of people also like to bring along folding chairs,
umbrellas, water bottles and perhaps string bags to
hold their wine purchases. Plastic cups (not glass!) are also a good
idea if you want to sip drinks.
And naturally, you can bring along a throw rug if you want to dine
out in the Park (the wide variety of inexpensive food in the Food Court will
please almost anyone - all meals are served with disposable containers and
cutlery).
There are also plenty of toilet facilities in the grounds, including
disabled facilities at the William Street end of the Park.