Awkward meeting with said child later when he/she tracks you down via Jeremy Kyle and asks how did you meet mommy.?
I suspect this is some type of tease/flirting, surely she has no intention of doing this, just attention, opportunity to catch someone's eye, out of the ordinary wg.
Advice would be to book an overnight with her £1600 before you commit to farthering her child
see if the chemistry is there, why does she not just ask for sperm to be sent to her in a cryogenically frozen bottle (at your expense )