General rules in disqualification of an animal for a korban
An animal must be Kosher in order to be eligible for use as an offering: Pesachim 48a; Temurah 29a
The child born from any animal which is invalid for Beit haMikdash use, other than that born from a mortally wounded animal, may be brought as an offering: Bechorot 7a; Temurah 30b, 30b-31a