On July 12, her 16th birthday, Malala will speak to the United Nations about the issue.
With the patch of skull missing, Malala is limited in what she can do.
Malala has made impressive strides and faced her medical treatment with bravery, Rosser said.
Headmistress Dr Ruth Weekes said she believed Malala needed the stability of being at school.
Malala Yousafzai, 15, was attacked in October after campaigning for girls' rights to education.
On Monday, doctors said they did not expect Malala to have to undergo any further surgery.
Another friend of Kainat's - apart from Malala - was also shot and injured.
Malala has asked to keep the bone once it has been removed, said Dr Rosser.
On Sunday, officials said Malala would remain hospitalized until she is well enough to be discharged.
"Malala's dreams represent what is best about Pakistan, " said Mr Brown, the former UK prime minister.
When he first met Malala, in tow with her father, she was kind of bashful.
Malala wondered on her blog if she should adopt a pen name -- Gul Makai.
She condemned the attack against Malala Yousufzai for which she expressed a deep sense of grief.
UNESCO: Malala Yousafzai honoured at UNESCO seminar in Pakistan
Malala's father Ziaududdin Yousafzai has been given a job at the Consulate of Pakistan in Birmingham.
Malala was shot in the Swat Valley as she travelled home from school with two friends.
Malala was flown to the Queen Elizabeth Hospital in Birmingham on Monday night for treatment.
Malala was then shot, as were two other girls who survived the attack with lesser injuries.
The attack on Malala prompted outrage and wide outpourings of support, in Pakistan and overseas.
Apparently, the list is much longer, and Malala clearly fit the bill as a Taliban target.
FORBES: Attack On Pakistani Teen Turns Nation Against The Taliban
Malala is in a critical condition two days after being attacked in the north-western Swat Valley.
Several students told Khan that they respect Malala but were concerned about their safety, he said.
Last month, Malala asked a graduate school not to name its institution after her.
Malala Yousafzai was transferred to a British hospital on 15 October for prolonged medical treatment.
Malala, now 15, rose to global fame after the attack which almost claimed her life last October.
The BBC's Shaimaa Khalil spoke to a friend of Malala's who was also injured in that attack.
Malala, known as a campaigner for girls' education, was shot in the Swat Valley on 9 October.
Malala was shot as she travelled home from school with two classmates in north-west Pakistan in October.
Malala was left in a critical condition, with her father later describing her survival as a miracle.
Since the shooting, Malala and her father have had threats made against their lives by the Taliban.
Malala arrived at the Queen Elizabeth Hospital (QE) on Monday after being shot by a Taliban gunman.
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