According to Isaac Klein, in his book A Guide to Jewish Religious Practice (Jewish Theological Seminary of America, 1979):
The usual practice is to erect the tombstone no sooner than one year after the death, since to do it earlier would be an indication that the memory of the deceased is fading and artificial means are required to revive it…In Western European countries and in America, it has become the custom to “consecrate” the tombstone with a service. Since in America the tombstone is covered with a cloth, which is removed by the family during the service, the ritual has been called the “unveiling.”
The unveiling usually takes place twelve months after the death. While there is no traditional basis for this service, except for custom of visiting the grave on the day of Yahrzeit, it is now an accepted and meaningful practice. It offers additional opportunity for the officiant to pay tribute to the deceased as well as to speak to the living about the meaning of life and death. Participants should take care to insure that the unveiling does not become a social event.
Alfred J. Kolatch, in his book Inside Judaism (Jonathan David Publishers, 2006), writes the following:
Although monuments have been erected over graves for many centuries, the custom of conducting a special unveiling ceremony was instituted toward the end of the nineteenth century in England and later in the United States to formalize and dignify the erection of the monument. The British use the term “tombstone consecration,” whereas Americans have adopted the term “unveiling.”
There is no religious obligation that an unveiling be held, and it is not necessary that a rabbi officiate. Anyone able to recite the selected psalms and deliver a eulogy, if one is desired, may conduct the ceremony.
Although an unveiling may be held at any time after the monument has been erected, most families wait about one year so as to give the earth a chance to settle.
Based on the above explanations—namely, that unveiling is a custom rather than halakhic (decreed by normative Jewish law), and a relatively recent custom at that—it would seem to me that an unveiling may be done at almost any time when the surviving family members deem it an appropriate time, and one in which everyone whom they would like to be in attendance can attend.