While I don't know the size were talking about, the Caroma toilets have a 4" trap way and will handle anything she can pass.
They are as clog proof as your going to get.
I have installed a few for people that have had similar problems without 1 call back. I have sold about 30 or so of them and I always sell them with a guarantee that says I will come out the first year for free to unstop the toilet if necessary.
I have yet to go out to do that.