Andre Villas-Boas' side headed into the weekend's fixtures third in the Premier League, just two points behind leaders and bitter rivals Arsenal after a great start to the campaign.
They are also impressing on the European stage, coming through their toughest Group K tie with ease on Thursday night as they saw off Anzhi Makhachkala 2-0 in near-freezing conditions in Russia.
The Europa League performance sets Spurs up nicely for their return to domestic action against West Ham on Sunday - just a day after captain Dawson penned a new three-year deal at White Hart Lane.
"It's been a great start, but it's early days and we've just got to keep it going," the 29-year-old said.
"We'll just keep playing and hopefully we'll keep playing with confidence, starting with West Ham.
"Things are going well at the moment, but West Ham will be a tough game. It's a London derby and I'm sure they will want to beat us. But we're looking forward to it.
"We're brimming with confidence at the moment. We've got a new squad full of top players and a top spirit in the camp. I think we showed that in Russia."
Villas-Boas made eight changes to the Spurs starting line-up against Anzhi, although the side was still awash with star quality.
Such strength in depth coupled with Tottenham's fine start to the season has led to suggestions the north London club can win the title.
"We're not going to get carried away," Dawson said. "You have to earn the right to finish up there and there are some top teams in this division.
"We've earned the right to be up there at this moment but it's early days. It's a long hard season."
The Europa League is a key target for Villas-Boas, with the bookmakers making them early favourites to win the competition.
The big question, though, is whether Spurs can compete successfully on domestic and European fronts.
"Well, we will certainly try," Dawson said. "We will give it a good go.
"We've got a big squad - we need one and it's paying dividends.
"You only have to see the team we put out in Russia - it was very strong.
"We want to win the Europa League and we want to finish as high as we can in the Premier League.
"The players are certainly showing the intent to do that at the moment. Long may it continue."