Unlike mammals, the Torah does not specify signs to differentiate between kosher and non-kosher birds. The Torah (Deuteronomy 14:11-21) lists twenty-four types of forbidden fowl (eg. owl). All other fowl are assumed to be kosher (eg. chicken).

The sages of the Mishnah however, do provide four signs to identify non-kosher fowl (Chullin 3:6). Since we lack the experience to apply these rules, for all intents and purposes we are permitted to eat only those birds that we have a tradition regarding their being kosher (Ramo YD 82:3).

Since we do not have a definitive tradition about the status of peacocks (peahens) - their status is in doubt, and they should not be eaten. The same goes for other birds whose status is in doubt. The eggs of any non-kosher fowl are also forbidden to be eaten.