Michelle Armstrong, of Kirwans Solicitors, which represented the family, said: "The CICA rejected the case twice, questioning whether the actions of a three-year-old perpetrator could constitute a 'crime of violence'.
"We argued that the age of the perpetrator was irrelevant when claiming compensation from the CICA. And it was on this point that we won."
Jay will now have psychological tests to see how the incident affected him, before the level of compensation is decided.
A spokesman for the CICA said it did not comment on individual cases, but said it made "payments to victims of violent crime as a gesture of public sympathy."
"To ensure that the application of the scheme is as robust as possible there are safeguards built in," he said.
"All cases are decided on their own merits and, if an applicant does not think their case was assessed fairly, they may apply to have it reviewed, which can then go to tribunal if there is a further dispute."
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