The move comes as the charity seeks to tackle what it claims is a growing complacency among the public following the introduction of the meningitis C vaccine.
Baxter said it was important to ensure the public were aware that meningitis has many different strains and that people can recognise the symptoms quickly.
She will have responsibility for PR and media relations, internal publications, advertising and liaison with celebrity patrons.
Baxter plans to focus her PR strategy on strengthening the trust's profile among health professionals and ethnic minority communities to combat ignorance of the disease.
'Research has shown that many people in ethnic communities don't believe the disease affects them - a misunderstanding (we) fear may cost lives,' said Baxter.
Leading a three-strong team, she reports to chief executive Philip Kirby, who said he expects her to ensure the charity is the first port of call for meningitis enquiries.
Baxter replaces Nicola Davies, who quit to join Gloucestershire County Council as media and PR manager in January.
Baxter will encourage greater understanding of the after-effects of the disease.
She will also handle communications campaigns around annual fundraising events, such as the charity's Toddle Waddle and Coffee Break.