I nobody ever gets fired, and the promotion probabilities are independant of gender, then i guess that eventually every body will get a promotion, and the gender distribution will be the same as the underlying population. You may need some kind of attrition mechanism in the upper promotion classes.
I think it may be possible to applay the theory of Discrete Markov Chains to this problem to derive analytic solutions. You could also use programming.
Ultimately you should try to come up with a matrix of what are called 'transition probabilities'. Look on the wiki page, there is no replacement for a picture in explaing transition matrix.
What are you programming in? I think matlab is probably best for something like this, cuz it has such nice matrix languge. R is a close second, and it is free.