Gayle King 's totally here for Taylor Swift ’s new docuseries and concert film ... telling TMZ she loves it ... but she admits there’s one thing that’s seriously bugging her!

We caught up with Gayle in NYC Monday ... and first things first, she’s making it clear she’s not fashionably late to the Taylor party -- she’s a full-on Swiftie, loving every behind-the-scenes moment in the docuseries.

But there’s one thing Gayle can’t get behind ... the docuseries landing on Disney+ instead of Paramount+ or CBS, where she hosts "CBS Mornings."

Catch the full clip -- Gayle spills on how she wanted that Taylor docuseries for herself, but also admits she can't wait to watch it. Gallery Launch Gallery Getty

And she’s not alone ... Taylor announced Monday on "GMA" that her six-part d

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