I hate to go off topic from the original post, but am very curious where you get this information about St. Dominic in relation to the origins of the Rosary?
In the Catholic Encyclopedia it seems to state otherwise (see the following paragraph and the link to the online Catholic Encyclopedia).
Of the eight or nine early Lives of the saint, not one makes the faintest allusion to the Rosary. The witnesses who gave evidence in the cause of his canonization are equally reticent. In the great collection of documents accumulated by Fathers Balme and Lelaidier, O.P., in their “Cartulaire de St. Dominique” the question is studiously ignored. The early constitutions of the different provinces of the order have been examined, and many of them printed, but no one has found any reference to this devotion. We possess hundreds, even thousands, of manuscripts containing devotional treatises, sermons, chronicles, Saints’ lives, etc., written by the Friars Preachers between 1220 and 1450; but no single verifiable passage has yet been produced which speaks of the Rosary as instituted by St. Dominic or which even makes much of the devotion as one specially dear to his children. The charters and other deeds of the Dominican convents for men and women, as M. Jean Guiraud points out with emphasis in his edition of the Cartulaire of La Prouille (I, cccxxviii), are equally silent. Neither do we find any suggestion of a connection between St. Dominic and the Rosary in the paintings and sculptures of these two and a half centuries. Even the tomb of St. Dominic at Bologna and the numberless frescoes by Fra Angelico representing the brethren of his order ignore the Rosary completely.
newadvent.org/cathen/13184b.htm