The actress - who is making television history as the first woman to play Doctor Who - made a very brief debut in the BBC sci-fi series in last year’s Christmas special when Peter Capaldi’s version of the character regenerated.
But her first full episode as the 13th Doctor aired on Sunday.
The instalment, aptly titled The Woman Who Fell To Earth, saw the Doctor meeting new companions Ryan Sinclair (Tosin Cole), Yasmin Khan (Mandip Gill) and Graham O’Brien (Bradley Walsh) after falling from the sky - and realising she was a woman.
When Yasmin refers to her as “madam”, Whittaker’s Doctor ask: “Why are you calling me madam?”
A puzzled Yasmin explains it is because she is a woman, and the Doctor replies: “Does it suit me?”
“Half an hour ago I was a white-haired Scotsman!” she adds.
Fans of the BBC sci-fi hit were quickly impressed with the Broadchurch star’s take on the beloved character.
“JODIE WHITTAKER IS KILLING IT AS THE DOCTOR,” posted one person on Twitter.
Another said: “I love her. I mean, genuinely. I love her. Not because she’s a woman. Because she’s THE DOCTOR.”
“Jodie is already my favorite Doctor,” said another.
“This production value and writing is everything I’ve always wanted this show to be. It’s taking itself seriously but still so much fun. I’m in love.”
“Listen. I’ve never been able to pick a favorite doctor-until now,” tweeted another.
“Thirteen is my fave. I already love everything about her so much. Jodie is the Doctor.”
Many said Whittaker was “perfect” for the part.
One said they had “fully forgotten that the Doctor was ever a man”.
Viewers also enjoyed Whittaker’s Huddersfield accent.
The actress previously said that, unlike other parts, she was never asked to do any particular voice for the Doctor, so she just stuck with her own.
“Good to hear a northern accent that isn’t gratuitous or for comic effect,” posted one appreciative viewer on Twitter.
Another posted: “So nice to get northern voices in roles like this. Love.”
Doctor Who continues on BBC One.