We examine gender differences in collaboration networks and academic career progression in physics. We use the likelihood and time to become a principal investigator (PI) and the length of an author's career to measure career progression. Utilising logistic regression and accelerated failure time models, we examine whether the effect of collaboration behaviour varies by gender. We find that, controlling for the number of publications, the relationship between collaborative behaviour and career progression is almost the same for men and women. Specifically, we find that those who eventually reach principal investigator (PI) status, tend to have published with more unique collaborators. In contrast, publishing repeatedly with the same highly interconnected collaborators and/or larger number of co-authors per publication is characteristic of shorter career lengths and not attaining PI status. We observe that women tend to collaborate in more tightly connected and larger groups than men. Finally, we observe that women are less likely to attain the status of PI throughout their careers and have a lower survival probability compared to men, which calls for policies to close this crucial gap.