SCOUTING REPORT T

DEMI Moore fangirled her way through daughter Scout out Willis’ set at the Alice + Olivia presentation on Tuesday.. The proud mama swayed to the music and gazed adoringly as her middle child strummed the guitar and sang. “Like ev-every mother, I do my best to show up for my kids whenever I can — it’s a pleasure for me,” the raven-haired actress tells The Post.

Deep-voiced Scout, 26, is dropping her first album next year. “It’ll probably be self-titled,” says the Brown Uni-versity grad, who rocked a snazzy Alice + Olivia silver se-sequined suit. “I’ve been self-producing and self-recording, and it’s just me and the guitar right now.”

She reveals that she’s discontinued her clothing collection, Scout’s General, for fear of spreading herself toooo thin. “I just realized that if I want to do music — which really is the most important thing in the world to me right now — that I had to focus on it and not have it be a secondary thing,” she says.

Also cheering her on was little sister Tallulah, one of eight female artists tapped to create an installation for designer Stacey Bendet’s Chelsea Hotel-themed show. “It’s about femininity and celebrating womanhood and that also comes from the internal,” says the 23-year-old, who posted a heart-rending Instagram in July celebrating her three years of sobriety and recovery from an eating disorder.

As for mother Moore’s creative endeavors: The 54-yearold has a cameo in “Love Sonia,” an upcoming drama about international sex trafficking costarring Freida Pinto. “It’s an important story to tell and get out into the world,” Moore says.