The West Yorkshire-born actress was revealed as Peter Capaldi's successor as The Doctor last month and has already spoken with fellow actors who have played the role.
Speaking to Shaun Keaveny on BBC 6 Music's breakfast show on Monday, Whittaker said taking on the role was "incredibly emotional because my entire life ... all I ever wanted to be was be an actor and I wanted to do it because I wanted to play pretend, and that is the ultimate."
She added: "I'm about to play an alien, a Time Lord. And that as a girl? Who knew? That's incredible and really emotional because of that."
Whittaker said taking on the role was "not in the realm of possibility ever, growing up".
"I've been asked so many times 'what's your dream part?' and I always try and articulate something that is outside of what people tell me I can only play, and now it's like 'see I told ya'," she added.
"The people that are in these roles that we are excited about, or passionate (about), or look up to, don't always have to tick the same box and that's what is really incredible about it.
Whittaker revealed she had missed the online reaction to the announcement as she does not use social media, but said friends had been sending her notable posts, including a video that went viral of a young girl overwhelmed by the news.
Asked about seeking advice from former Doctors, Whittaker said she knew several of them and they had shared what a unique experience it was, adding "There's only a few people who know what it's like.
"I think the overwhelming sense of this is it is such an exciting journey you're about to go on and it's to be enjoyed," she added.
"They know I don't know yet, and I think that's the fun. There's no advice you can give because no person plays this part the same.
"What a freeing thing for my day one and I'm on set. I'll be right okay."
She added that the show's new writer, Chris Chibnall - who she worked with on ITV's Broadchurch - would be "amazing".
"I already know how incredible he is, but just to know he's coming from a fan point -of-view of the show - and so the direction he's going to take it is going to be amazing."
Whittaker may be heading for worldwide fame as the first female Doctor Who – but before taking up the role is playing a very different doctor indeed.
After getting plenty of criticism from a minority of Doctor Who fans who believed a woman couldn’t play the role, Whittaker’s new BBC drama series Trust Me beginning on Tuesday shows her playing someone who genuinely shouldn’t be a doctor – a nurse who steals a friend’s identity to land a top hospital job.