Hi Sonya
Interesting question - don't remember hearing it asked before. I suppose, at a pinch, any (presumably baptized) believer can baptize any other (unbaptized) believer!
Usually its leaders that do it; and it seems to be the same in the Bible, but I don't think the Bible gives any rules on it at all. It would seem only right (in normal circumstances) that those in leadership, or more mature, should be asked to do it - out of mere courtesy to them as leaders. But there could be circumstances when this isn't possible, or there's no time.
When Philip baptized the Ethiopian (Acts 8)there is no mention of anyone else, except those two. The Ethiopian would have had a retinue of attendants with him but they were apparently not involved). Phillip gave him the Gospel, he believed, and he was baptized by Phillip, that's all!
Jeannette