Since baptism is a Sacrament are the laity allowed to baptize?
Yes. The 1979 Book of Common Prayer states “In case of emergency, any baptized person may administer Baptism according to the following form. Using the given name of the one to be baptized (if known), pour water on him or her saying, ‘I baptize you in the Name of the Father and of the Son and of the Holy Spirit.’”
This is followed by the Lord’s Prayer and any other appropriate prayers. The person who administers the emergency baptism should inform the priest so that the baptism may be properly registered in the Church. If the one baptized survives then there should be arranged a public celebration of the Sacrament with a priest presiding and all elements of the baptismal rite used except for the administration of water. This allows the person to make a public confession of Jesus, receive chrismation, and be received by the Body of Christ. I once had the privilege of doing this for a woman who had been given an emergency baptism by a nurse just after her birth and she completed her baptism some 50 years later.