If offering Duha prayer will not affect the work for which you are responsible, then there is nothing wrong with offering the prayer.

The Sunnah indicates that it is mustahabb to pray two rak‘ahs between each two calls [adhaan and iqaamah], and the basic principle with regard to Islamic rulings is that they include both men and women, so long as there is no evidence to indicate that the ruling applies exclusively to men and not to women, or vice versa. There is no evidence to indicate that this matter applies only to men, to the exclusion of women, so the ruling remains as is, which is that praying two rak‘ahs between the adhaan and iqaamah is mustahabb for both men and women, whether that is in the mosque or at home.

The best is to pray only the Sunnah prayer of Fajr, and that takes the place of tahiyyat al-masjid, just as the obligatory prayer also takes the place of tahiyyat al-masjid.