Is it wrong for a woman to baptize someone?
The command to teach the gospel to lost souls and baptize them was given to ALL Christians, not just males (Matt. 28:19; Mark 16:15).
True, women are commanded to not teach or exercise authority over men (1 Tim. 2:11-12), but that command is limited to within the church (1 Tim. 3:14-15). No one is within the church until AFTER baptism (1 Cor. 12:13; cf. Eph. 1:22-23). Thus, no scripture prohibits a woman from teaching the gospel to anyone who is lost – male or female – and baptizing them into the church.
However, if this freedom a woman has offends a brother or sister weaker in knowledge, she should give up her freedom for the sake of unity (Rom. 14:1-15:2).