As someone else said, she didn't look pregnant at the SAG awards, so she probably had the baby sometime before that. But in a new interview with Scott Patterson, he mentions that Alexis is a new mom, so she definitely has already had the baby
http://www.glamour.com/story/gilmore-girls-scott-patterson-on-luke-and-lorelai-relationship-in-netflix-revival
Scott mentions that Alexis had a son
What was it like to see Alexis all grown up? She was like 16 when she started this show and went on to have a great career and get married and start her own family.
SP: It was great to see her. She's really blossomed as a woman and now she's a proud new mother and married and happy. I remember her as an 18-year-old kid, fresh out of college coming into Hollywood and being a little overwhelmed. She's just the most likable, intelligent person and adorable human being. She hasn't changed at all. She looks the same. We're comparing notes because my son is about a year and a half older than her young son. I’m showing her photos and videos and what to expect. We're just really enjoying each other’s company.
Scott mentioned that his son is a year and a half older than Alexis's son. Scott's son was born in summer 2014 (I think June), so Alexis probably had her kid sometime between October and December, maybe early January.
Alexis seems like a private person, so that's probably why there was no official announcement. Her and her husband secretly got married too if I recall, so they probably just prefer privacy and keeping to themselves.
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