Hey Suzy,
Unfortunately I there is no direct route by bus from Australia Zoo to the Brisbane Entertainment Centre. However, you are definitely able to mix train and bus travel to see through your journey.
Your best bet would be to go to the Translink webpage: http://www.translink.com.au/
On the right hand side of the screen, there should be a little box called "Journey Planner." Simply type "Australia Zoo" into the "From" section, and "Brisbane Entertainment Centre" into the "To" section, then select the time & day you wish to travel on, and it will bring up all your options.
So for example, you could leave Australia Zoo by bus at 10:11am and arrive at Glasshouse Moutains Railway Station at 10:23. From there you catch the train at 10:39 to the Northgate Railway Station, and from Northgate you change trains to one that will take you to Boondall (where the Entertainment Centre is), arriving there at 11:47. And it'll only cost ya $6.70.
There's heaps of options for all times of the day though, so check out the website to suit your travelling times.
:-)