Generating QQ-plot for custom random number generator

I would like to generate a QQ-plot for a (discrete) custom random number generator. The generator only has a probability function predefined and I use this function to generate a table which I then search in based on a value from U(0,1) (essentially using the inverse-transform method, with a binary search).

The problem is, I have no way of generating a set of data, which could be used to verify the random numbers I generate myself -- is there a way to generate a set of values which may be used to generate a proper QQ-plot, with just the probability function?

So far I've tried by creating a histogram and plotting it against the probabilities of the distribution... which is not what I should be doing.