Context. Asteroid families are the outcomes of disruption or cratering events on a size and energy scales that are not reproducible in laboratory experiments. Overall structure, as well as properties of individual members, in the old families could have been changed since their formation. Therefore young families preserve best the characteristics of the initial event. Aims. We study the most suitable known asteroid family with an age of less than 1 Myr, the Datura family. We aim (i) to obtain information about rotation state and shape of the largest members in the family; and (ii) to constrain its debiased population down to couple of hundreds of meters in size. Methods. We have analyzed the up-to-date catalog of orbital elements of main belt asteroids. We evaluated the detection efficiency of Catalina Sky Survey (CSS) in regard to detections of members in the Datura family, and we have used our photometric observations and lightcurve inversion methods to determine the rotation states and shapes of the largest members of the family. Results. We determined rotation periods of the seven largest members of the Datura family, and we also derived accurate mean absolute magnitudes for six of them. Except for the largest fragment (1270) Datura, the asteroids tend to have long rotation periods and large amplitude of the lightcurve, witnessing an elongated shape. For the four largest asteroids, our observations allow us to resolve rotation pole and a rough shape. All of them are prograde-rotating and have the latitude of the rotation pole >50°. Our search in orbital catalogs resulted in the discovery of many small, sub-kilometer members of the Datura family. Using the CSS detection efficiency, we inverted this information into the debiased population of Datura family members. We show that the mass and angular momentum content in small fragments is negligible compared to the largest fragment (1270) Datura. These findings may help to constrain the formation mechanism of the family.