Police said accelerant was poured through the letter box of a house at St Agnes Place and set alight at about 22:30 BST on Wednesday.
The fire was put out before emergency services arrived. It damaged the front door and caused some smoke damage to the house.
The children, and two women aged 23 and 61, were unharmed.
Police said they are working to establish a motive for the attack and want to hear from witnesses. Detectives can be contacted at Musgrave Police Station by calling 101.

Earls was dismissed for a dangerous tackle on Fraser Brown playing for Munster against Glasgow Warriors in the European Champions Cup.
A "timely" guilty plea and expression of remorse helped in an initial four-week ban being reduced by half.
Earls is also suspended for Munster's Pro12 match against Ulster on Friday.
Referee Jerome Garces dismissed Earls 19 minutes into the Pool 1 game at Thomond Park.
The game in Limerick was Munster's first since the death of head coach Anthony Foley in Paris.
Earls was cited under the law for "lifting a player from the ground and either dropping or driving that player's head and/or upper body into the ground while the player's feet are off the ground".
An independent disciplinary committee found that the offence was at the low end of World Rugby's sanctions and selected four weeks as the appropriate entry point for a suspension.
"As there were no aggravating factors, the committee then reduced the sanction by a maximum of two weeks due to Earls' timely guilty plea, expression of remorse and clean disciplinary record before imposing a suspension of two weeks," the committee said.
Ireland take on the All Blacks in Chicago and Earls, who has the right to appeal the decision, will be available for the Test against Canada on 12 November in Dublin.

At one point, she says, "there was no-one to turn to in the school and I felt so low I didn't want to go on".
According to research for BBC School Report, half of teenagers with mental wellbeing issues try to cope alone.
And a third said they were not confident enough to speak to a teacher.
At her lowest point, Grace made a "suicide video", which she posted on YouTube.
"I'd get beaten up every week," she says.
"Teachers wouldn't do anything. I even heard the teachers talking about me behind my back."
According to her mother, Sarah, Grace got some help through external music therapy and counselling but little support directly from her first two schools.
Support is better at her third school, where she helps as an anti-bullying ambassador.
She is also a member of the National Anti-Bullying Youthboard.
ComRes researchers questioned a representative sample of more than 1,000 UK-based 11- to 16-year-olds for BBC School Report:
They said the most important thing schools could do to support pupils' mental wellbeing was to provide someone trustworthy to talk to confidentially, but:
Separate research on just over 700 teachers found:
In January, Prime Minister Theresa May announced plans to transform attitudes to mental health, with a focus on children and young people.
The plans include better links between schools and NHS specialist staff and mental health first aid training for every secondary school.
Reacting to the School Report research, Edward Timpson, Minister for Vulnerable Children and Families, said the government would "transform mental health services in schools" and was commissioning research to help schools identify which approaches worked best.
"Growing up in today's world can be a challenge for children and young people, so it's vital that they get the help and support they need," said Mr Timpson.
Last year, research for the children's commissioner for England suggested more than a quarter of children referred for mental health support received no treatment.
And on Thursday, commissioner Anne Longfield said the School Report study highlighted "many desperately sad stories" of children with serious conditions being denied support.
She called for urgent action from schools, the NHS and government.
The Family Links and Nurturing Schools Network said schools needed better staff training and enough resources to support and improve pupils' emotional and mental health.
"We must go further to invest in preventative approaches in schools and at home," said the network's chief executive, Nick Haisman-Smith.
Three children aged between four and six and two women have escaped injury in an arson attack in west Belfast.
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Ireland wing Keith Earls will miss the Test against New Zealand on 5 November after being suspended for two weeks following his red card on Saturday.
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Grace, 16, has been bullied for the past nine years, has moved schools twice, struggled with suicidal thoughts and taken medication for anxiety and depression.