The church's sole requirement is that a Godparent (Sponsor) must be a member of the Eastern Orthodox church in good standing. That's all to the best of my knowledge. Typically, parents await to be asked by someone to be a sponsor for their child.
In Greek practice, the first born child would be sponsored by his or her parents Sponsor (Combaro) from their wedding.*
The practice, not common these days, of a married couple who are or intend to be sponsoring more than one child, to rotate who will be the Godparent, the men sponsor girls, women sponsor males. The theory is that if a male and female as adults are attracted to each other, they would not be prohibited from marriage because they are God-brother and God-sister. This is a practice, not a teaching of the church.
Here's another tradition which is not practiced these days, from what I've seen. GOAA Bishop Maximos of Pittsburgh enforced this practice in the GOAA Metropolis (Diocese prior to 2003) of Pittsburgh. It was the tradition that there be only one Godparent. There was traditional support for this practice, and while I recall from where I read it, I have no idea where it is now (it was reprinted in the monthly publication of my parish, many years ago). Because "the two...become one," through the Sacrament of Holy Matrimony, Metropolitan Maximos permitted two Godparents if they were married.
Again, the church's rule is only that a member in good standing sponsor an individual. The church has no rule about whether the sponsor should be a male or female.
I would suggest when your baptism becomes imminent, I don't see anything wrong with asking the lady whether she would be interested in serving as your sponsor. When word gets out about your baptism, someone else might come forward and it is difficult to refuse such a blessed offer.
My experience and knowledge comes from GOAA practice only. I'm not aware of variations in other jurisdictions. My experience is based on serving as the chanter in my parish at all baptisms, wherein I assist the priest in directing the logistics of the sacrament, during the past 36 years.
*I'm only too aware of this practice. My parent's friends assumed that my Dad's Combaro, his Army buddy, would be my Godparent, but because he lived out of state, my parents wanted a local Godparent for me. Luckily, my aunt told someone who was having problems bearing her own child that no one had come forward to sponsor me, so they asked my parents, which resulted in a blessed arrangement for all concerned; "May their Memory be Eternal." (I was 2 years old when I was finally baptized due to the delay.)
