Get a quality aluminum frame with carbon fork, carbon seat post. the rest is up to your budget. Wheels, wabi makes a light inexpensive wheelset. You can always get some cheap 20mm carbon clinchers which would weigh around 1500g.

You also can get a 20lb bike that is safe and affordable to ride for a lot less than a weight weenie build would be. Most of the girls I roll with lift weights so they have no problem with heavy bikes, maybe a trip to the gym would be more beneficial than a lightweight bike.

here is a <18lb QUALITY bike - Wabi Cycles Lightning SE fixed gear bike specs

Chinese carbon track frames [no idea on how the quality is, would be a risk]