Walker, who only joined the League Two side on loan from Watford until January 5 on Friday, curled in a free-kick after 24 minutes before sub Yemi Odubade made the game safe , while Dons' Ed Harris collected his second yellow card.
"Josh only came in on Friday and it was a tremendous debut," said Westley. "He was excellent in possession of the ball and he was very composed and it was a tremendous goal as well.
"The last time I went into the third round draw as a manager we drew Darlington, it wasn't the one I wanted and I gave up on worrying about the draw at that stage so we will take what we get now.
"AFC Wimbledon are top of their league and we didn't underestimate them. They are bright and they are incisive and top of the league for a season."
And AFC Wimbledon manager Terry Brown said: "If we were going to lose to anyone it is better that it was Stevenage than that lot up the motorway."
Source: PA
Source: PA