The neighbours entered the burning property in Milford Drive, on Sunday afternoon in an attempt to rescue two cats, police said. The occupants were not home at the time.
The women had inhaled smoke and were taken to hospital with breathing difficulties. The cats were unharmed.
Fire destroyed the front door and caused heavy smoke damage to the house.
Dorset Police said it believed the fire had been started deliberately through the cat flap in the front door of the property at about 15:00 BST.
Officers are appealing for witnesses or anyone with CCTV to get in touch.
Det Con Luke Davis said: "I am appealing to anyone who saw suspicious activity near to the property during that afternoon, particularly anyone seen in the garden or the front drive of the property just before 3pm, to please contact me.
"If you have any information about the cause or motive of the fire, please contact Dorset Police or call Crimestoppers anonymously."

Gary Price was suspended from all council duties for five months in November after Powys council's Standards Committee ruled he had breached the code of conduct.
His appeal has been dismissed by the Adjudication Panel for Wales following a two-day hearing in Llandrindod Wells.
Mr Price has been contacted for comment.
He was found to have sent information which the council said "incorrectly and unfairly" portrayed what happened at a grievance appeal hearing, in which he was a panel member.
The Adjudication Panel for Wales unanimously agreed to refer the matter back to the Standards Committee with a recommendation that Mr Price be suspended for three months.
Council leader Barry Thomas said the decision "sends out a clear message that those who enter public office have to operate within the members' code of conduct and maintain the highest possible standards".

The White Garden, at Kensington Palace, was planted to mark 20 years since Princess Diana died in a car crash.
The Duchess of Cambridge joined the princes on the garden tour.
A spokeswoman for Kensington Palace said: "The engagement will allow the princes to pay tribute to the life and work of their mother."
They met representatives from the causes and charities supported by Diana, including the Royal Marsden and Great Ormond Street hospitals, the National Aids Trust, Centrepoint youth homelessness charity and the Leprosy Mission.
Members of the public have been leaving tributes and flowers at the gates of the palace to mark the anniversary of Diana's death.
The Princess of Wales died on 31 August 1997 in Paris, when William, now the Duke of Cambridge, was 15 and his brother was 12.
The garden at their mother's former home has been inspired by memories of her life, style and image, such as her white "Elvis" Catherine Walker dress.
The White Garden, as it is known, follows a tradition first established at Sissinghurst Castle in Kent, famous for its own white garden created in the 1930s.
Their Royal Highnesses met gardener Sean Harkin who designed the display and Graham Dillamore who knew the princess when he worked there some 30 years ago.
The garden has been open since spring and will continue into September with white roses, lilies, gladioli and cosmos.
It is the fourth London memorial created in tribute to Diana - the others are the Diana Memorial Playground at Kensington Palace, the Diana Memorial Fountain in Hyde Park, and the Diana Memorial Walk at St James's Palace.
Two women have been rescued following a suspected arson attack on a house in Bournemouth.
[NEXT_CONCEPT]
A decision to suspend a Powys county councillor has been upheld.
[NEXT_CONCEPT]
Prince William and Prince Harry have visited a London memorial garden for their mother on the eve of the 20th anniversary of her death.