Respiratory health is directly linked to the structural and mechanical properties of the airways of the lungs. For studying respiratory development and pathology, the ability to quantitatively measure airway dimensions and changes in their size during respiration is highly desirable. Real-time imaging of the terminal airways with sufficient contrast and resolution during respiration is currently not possible. Herein we reveal a simple method for measuring lung airway dimensions in small animals during respiration from a single propagation-based phase contrast x-ray image, thereby requiring minimal radiation. This modality renders the lungs visible as a speckled intensity pattern. In the near-field regime, the size of the speckles is directly correlated with that of the dominant length scale of the airways. We demonstrate that Fourier space quantification of the speckle texture can be used to statistically measure regional airway dimensions at the alveolar scale, with measurement precision finer than the spatial resolution of the imaging system. Using this technique we discovered striking differences in developmental maturity in the lungs of rabbit kittens at birth.