Do babies develop chickenpox immunity if they got the disease at less than 1 year of age?

My friend's daughter might be infected with chickenpox, since her older brother had it and he was staying pretty close 2 her. Its still too early to tell though. She's around 5 months of age. In case, she got chickenpox, would she develop the immunity for life for it at this early age? Please provide me with informative sources if availble. Thanks!
Answer:
Yes. Beyond the 4 months of age, the immune system of a child starts to develop. That's why people start their children for active immunization shorts around 4-6mos. Although people get immuned to chicken pox, they don't get immuned to Shingles which is caused by the same virus of chickenpox.

---

i had chicken pox twice. once under the age of one, and then at 3.. so that's a big NO for me. I dont think it means you are absolutely immune. some kids who get the vaccine get pox too.

---

anyone at any age who once had chicken pox will get immunity to it. it doesn't matter at what age a person had it., but if it is an adult - he/she will suffer a lot. small children do not suffer that much

---