Estimating the model (or at least analyzing the outline of the output) will be helpful. You can always check after estimating the model whether you're able to answer your question or not.

As from the design it is clear that it does not include time & one can't vary the probabilities by time. The ideal equation to answer all questions is:

P(death by day 13 on dose [MATH] d_{i}) = (1+exp[-(\alpha_{1} + \alpha_{2}logd_{i} + \alpha_{3}S + \alpha_{4}S*logd_{i} + \alpha_{5}t)])^{-1}[/MATH]

Deviance is a goodness of fit statistic & it would only tell you how good is the fit but does not tell you whether your model answers your question.

I'm not sure where the logistic link function log(pi/1-pi) comes into play here where pi = Probability of mortality, but i know it's equal to alpha + beta*logD or *D? where D is the dose.

Logistic link function when readjusted to leave just pi on the left hand side is the same as your given equation. So log model is no doubt appropriate to answer the question of finding probability of death by day 13 on dose di & also for finding the difference in probabilities for male & female.

The difference between male & female can be found by:

Marginal effect = Prob(Y = 1| S = 1) - Prob(Y = 1| S = 0), where denotes the means of all the other variables in the model.