The North London rivals were drawn out of the hat together on Sunday for what is arguably the standout fixture of the round.
Spurs make the short trip to the Emirates Stadium to face the Gunners on January 4.
"It's a special game and a massive draw so early in the competition," Dawson told the club's official website.
"We lost there earlier in the season and that was obviously a huge disappointment. I thought we played well that day. The FA Cup is different and this is certainly the tie of the round.
"We know all about Arsenal and what this game means to everyone. We'll go there looking for a positive result."
Tottenham lost 1-0 at Arsenal when the teams met in the Premier League back in September.