It is permitted initially to wear a new garment, get a haircut, and do everything you need. We add the words of the prince of halakhic decisors, Rabbi Moshe Feinstein of blessed memory (Igrot Moshe, Yoreh Deah Vol. 2, Siman 137), who suggested that there is room to say a woman may get a haircut during the Omer without any concern or doubt. After all, even during the thirty days of mourning (Shloshim), there is a dispute whether a woman may cut her hair, and Maran the Shulchan Aruch (Yoreh Deah 390:5) rules that she is permitted to do so. If so, the days of the Omer should not be more stringent than actual mourning, and we should permit a woman to get a haircut throughout the Omer initially. While Maran the Rema (ibid) forbade this during mourning, regarding the Omer, there is room to say even he would permit it. In any case, for the sake of a Mitzvah (commandment), such as an engagement and the like, she is certainly permitted initially to get a haircut and wear a new garment.