The League One side will travel to Old Trafford on Tuesday to face the Red Devils in the quarter-finals.
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Dobson and his fellow Addicks have already beaten Premier League opposition to get to this stage, knocking out Brighton 4-3 on penalties in the last round.
It was a memorable night for Charlton, and Dobson is full of belief that they can get seal another huge win in the competition.
Speaking to PA, the 25-year-old said: "It was a brilliant evening against Brighton and then to get the draw we did was obviously unbelievable.
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"We could win in normal time but if we have to settle for pens, I fancy us."
The visit to Old Trafford will not be the first for Dobson, who has already been to the Theatre of Dreams with West Ham as a fan.
"I have been Old Trafford a couple of times," he revealed.
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"I am a West Ham fan so I have been a couple of times to watch them.
"I actually went this season and watched the game up there, so I've been as a fan but walking out at the tunnel and playing, especially in the quarter-finals of the cup will be a completely different experience.
"Old Trafford is up there with Anfield as one of the most prestigious stadiums in England, obviously the biggest crowd, so it will be a wonderful evening for everyone involved in the club."
Dobson, who had a spell with the Hammers, saw Dimitri Payet's stunning free-kick at United in the FA Cup that season.
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It forced a replay back at Upton Park but the Hammers lost 2-1, with United going on to win the competition altogether.
The Charlton star will be keen to get revenge, but the south east London side could be stopped in their tracks by the in-form Marcus Rashford.
During his youth days at Arsenal, Dobson played against the England international, who is 15 days his senior.
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He recalled his encounters against the forward, who is now one of United's key players following a difficult campaign last term.
"Yeah I played against Rashford in the youth teams. I just remember him being so sharp. He wasn't the tallest but I remember him being so sharp.
"Then he obviously broke through and has done what he has done. This season he has been in unbelievable form so if he plays it will be a big test for us but one we are really looking forward to.
"He obviously had a dip in form for a period of time but he is an unbelievable footballer.
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"With his pace, quality on the ball and finishing, he has a bit of everything. It has come back together again this season under Ten Hag so he will be a huge threat."
Charlton are set to bring a large following to Old Trafford for what could be one of the most special nights in the club's history.
The last meeting between the two sides came in 2007, back when the Addicks were in the Premier League.
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"It will be an unbelievable atmosphere taking nearly 10,000 Charlton fans and a special evening for everyone involved," said Dobson.
"Obviously going to Old Trafford, we take belief that we have beaten Brighton and you have got to dream in football because you never know what can happen."
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