Malala "is now well enough... she is happy, in fact, keen for us to share quite a lot of clinical detail with you," Dr David Rosser told reporters.
"She's communicating very freely, she's writing," he said.
The girl has managed to stand with help for the first time since the October 9 attack.
Malala was "doing very well" but there were still some concerns about her smooth recovery, he said, adding that she was "not out of the woods" yet.
The schoolgirl, who along with two of her classmates was attacked in the restive Swat region of northwest Pakistan as they made their way home from school 10 days ago, was flown to the UK on Monday following a surgery at a Pakistani hospital during which a bullet lodged near her spine was removed.
"She is still showing some signs of infection, which is probably related to the bullet track. (There is) some infection in the bullet track, which is our key source of concern," Dr Rosser said.
Teams of specialist doctors looking after Malala feel that she will need a few weeks to rehabilitate and for her infection to clear up, following which part of her skull will need to be reconstructed either by reinserting the bone that was removed or with a titanium plate, BBC reported.
Earlier in the day, a hospital statement said Malala's condition this morning was "comfortable and stable".
"The 15-year-old, who sustained her injuries 10 days ago, is being treated at the Queen Elizabeth Hospital Birmingham with a team from both the Queen Elizabeth and Birmingham Children's hospitals looking after her," it said.
Earlier, media reports had mentioned Malala's age as 14.
"Malala's family remain in Pakistan at this time," the hospital statement said.
The number of support messages for Malala on the hospital trust's website has grown to more than 2,300 overnight, it said.
The Queen Elizabeth Hospital Birmingham Charity has set up an account within the main hospital fund to support Malala, who is widely known as a campaigner for girls' education in Pakistan