Immune competence is a key factor in the health and resilience of dairy ruminants. The aim of this study was to study immunoglobulin G concentration in serum shortly after birth and in colostrum of lactating animals as proxy of passive immune transfer and colostrum quality, respectively, and thus provide new health and resilience indicators for selection. Data from 424 female kids and 203 primiparous goats, reared on an INRAE experimental farm, were analyzed. IgG concentration was measured in kid serum and goat colostrum, respectively, using the radial immunodiffusion technique. Linear models were used to identify factors of variation in serum and colostrum IgG concentration, and health events were monitored for 5 weeks after birth to measure the impact of passive immune transfer on kids' health. We found a significant effect of serum IgG level on hindquarters cleanliness score (as a proxy of digestive troubles) and nasal and ocular discharge. As expected, the absorption of IgG in the days following birth is essential to ensure the passive transfer of immunity from the mother to the youngster, and provide immune protection. Genetic parameters were estimated for serum IgG concentration in kids and for colostrum characteristics in primiparous goats. Heritability of serum IgG in kids was not significantly different from zero. This low value, with large SE, may be due to the limited sample size and large environmental variability likely not accounted for. Especially, we could not adjust for the amount of IgG that was ingested by the kid, which can have a significant effect on serum IgG and possibly on heritability estimates. Heritability of colostrum traits were moderate, with estimates of 0.25 (±0.16), 0.35 (±0.16), and 0.25 (±0.16) for IgG concentration, IgG mass and colostrum volume, respectively. Genetic correlations with milk production showed high standard errors due to small numbers. However, estimates suggest a negative genetic association between production and IgG concentration in colostrum (rg = -0.44 ± 0.33), probably linked to a positive association with total colostrum volume. The significant heritabilities that were estimated for the first time demonstrate the existence of genetic control of colostrum quality in goats, and open up opportunities for selection in this species.