Yes, you can visit it! On days when parliament is sitting, there's a tour at 2pm, or you can watch from the public gallery. On Mondays to Fridays when parliament isn't sitting, there are tours at 1pm, 2pm, 3pm and 4pm.
The tours take a little over half an hour, and you need to get there a little in advance as you need to clear security. The entrance is through the Parliamentary Annexe Building, located on Alice Street opposite William Street. (It used to be through an entrance on George Street from the City Botanical Gardens, but has moved). Tours are limited to 30 people, but apparently aren't usually full. The general public can't book, but special groups need to.
The tour gives a bit of history of the parliament and the state, visits the grand staircase and both chambers, along with a few other interesting things. It's well worth going on!
(One thing to note though, is that there are no tours during the closed period of about two weeks over Christmas. The tours website doesn't mention that, if you're trying to visit around then check the rest of the site for the closure dates to make sure you avoid them.)