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Kelly Clarkson brought out an exciting new star to her Vegas residency ... but, tickets for her tour won't be coming out anytime soon -- 'cause she's still got to get through middle school.

The singer-songwriter took the stage at her "Studio Session" residency at Caesars Palace's Colosseum ... and, she told the crowd she had a special guest to serenade them.

Her 11-year-old daughter, River Rose , came out ... and, together, they belted out Clarkson's "Heartbeat Song."

Check out the clip ... the Kelly's leaning in close to help her little girl harmonize with her -- and, River puts in a really strong performance for someone so young. Gallery Launch Gallery Getty

As for how the audience reacted ... they seemed really positive -- whooping it up while the two performed tog

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