Hi
I just received a reply from this person and she included some answers from various web sites. Looking through these sites, basically they are saying that although an elder usually should perform a baptism, there is nothing in Scripture saying that another Christian cannot baptize.
One site said that he as a pastor often lets a father baptize their children with his instruction.

On my own search, I did notice that the WCF say that only elders should baptize. I have looked in the LBCF, but so far haven't been able to find anything on this aspect.

Tom