While we do not know Undauntra's House, we might speculate that given her awareness of the defensibility of a structure, it is one of the more martial ones; perhaps Dzur.
Her name sounds like it is meant to evoke the English word "undaunted" (undismayed, "not forced to abandon purpose or effort"), again evocative of heroic Dzur or perhaps persistent Tsalmoth ("Tsalmoth maintains though none knows how") or ambitious Tiassa.
We can also eliminate a few Houses as being highly improbable : Not Lyorn or Issola or Yendi (who would have spoken in a more genteel and circumspect manner than her direct bluntness), not Dragon (since no lineage is mentioned - although she might predate the custom of Dragons using lineage in their names), not Teckla (who apparently form a republic when they receive the Orb).