Spurs will go into the third-round tie on the crest of a wave following their 2-1 win at Manchester United on New Year's Day as they continued their improvement since Tim Sherwood replaced Andre Villas-Boas as boss.
"We never go anywhere with fear, especially Arsenal," said Dawson.
"It's a north London derby. We know what that means to the fans and to the players.
"There's immense pride for all of us in pulling that white shirt on, playing for the team and each other. That's what we'll be doing on Saturday.
"Sometimes things don't work out as well as you'd like but that's when you've got to stand strong as a team and the quality comes out when you can show the determination we did on Wednesday.
"We've never written ourselves off. People can say what they want but we've bounced back from those disappointing results.
"We knew even then that we were still right in the mix, although we are not going to get carried away just because we've gone to Old Trafford and won.
"We know we've got the FA Cup game against Arsenal and then Palace in the league.
"We'll keep plugging along, keep working and hopefully keep picking up results."