Here are the pertinent provisions of the General Instruction of the Roman Missal (1962) in English:
V - Votive Masses on the External Solemnity of Feasts356. The "external solemnity" of any feast means the celebration of the feast without an office, for the good of the faithful, either on the day on which the feast is impeded, or on a Sunday when the feast occurs during the week, or on some other established day.
357. An external solemnity either belongs to a feast by right or is granted by a special indult.
358. An external solemnity belongs by right only to:
a) the feast of the Most Sacred Heart of Jesus, on the 3rd Sunday after Pentecost;
b) the feast of the Blessed Virgin Mary of the rosary, on the first Sunday of October;
c) feasts of the 1st or 2nd class which are connected with some special liturgical service, if that liturgical service is transferred to a Sunday with the approval of the Holy See, only for the Mass which is celebrated in connection with the aforesaid liturgical service;
d) the feast of a duly constituted principal patron;
e) the anniversary of the dedication of the church itself in which the Mass is said;
f) the titular feast of the church itself;
g) the titular feast of the order or congregation;
h) the feast of the holy founder of the order or congregation;
i) feast of the 1st and 2nd class which are celebrated with an especially large attendance by the faithful; of this matter the local ordinary is the judge.
So, it is permitted to celebrate the Dominican Rite Mass of St. Dominic on the following Sunday. As a first-class Mass, the Sunday would not be commemorated by a second collect as first class feasts only permit an extra collects for "privileged memories" (e.g. ferials in Advent and Lent) and Sundays after Pentecost are not privileged. In addition, one should remember that an "External Solemnity" is a Votive Mass, not a transferred feast. So, if you have a celebration of St. Dominic on the following Sunday, the Mass and Office on August 4 is still that of St. Dominic.
It might also be useful treat another question here as well. Can the celebration of the the major feasts in the U.S. that are not holy days of obligation, which are moved to Sunday in the New Rite, also be celebrated in Dominican Rite on the Sunday? These feasts are Epiphany, Ascension, and Corpus Christi. Following the same principle, as there is permission granted to do so by the Holy See in the rubrics of the New Missal, and that would be equivalent to the permission of 358c above, it is my opinion that they may be so celebrated. As holy days of obligation are matters of canon law, not rubrics, the current discipline as to Mass obligation applies, not that in force in 1962.
One final matter for those using the 1962 Dominican Rite Breviary: the Office is not transferred under the rubrics for an external solemnity. Rather, the Office of the proper Sunday is used, which would be the 10th after Pentecost (1962 Missal) or the 8th after the Octave of Trinity (1933 Missal). And the Mass and Office of the proper day of the feast remain those of the feast. And remember in any case that one is never obligated to celebrate an External Solemnity Votive Mass; such Masses are merely an option.
May God grant all the brethren his choicest blessings on the feast of St. Dominic, whichever day they celebrate it on.