Beere, 22, has played 28 games for Dons, whom he helped win promotion to League One last season, including 15 appearances this season.
The Londoner has spent time on loan at non-league Bishop Stortford and Hampton & Richmond Borough.
He is in the squad for the Tynesiders' trip to Chester on Saturday.
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AFC Wimbledon have loaned midfielder Tom Beere to National League side Gateshead on an initial one-month deal that will expire on 11 March.