Officers are organising extra patrols around the south-west Dublin suburb, while detectives in Limerick are gathering intelligence on the McCarthy-Dundon gang.
Gardaí suspect that Melanie, who also went by her mother’s surname McNamara, was not the intended target.
She was a back-seat passenger in a stationary car on Brookview Way in west Tallaght at about 10.35pm on Tuesday when a 4x4 pulled up.
A gunman took out a shotgun and fired twice into the car, hitting Melanie once in the head.
Detectives suspect her 21-year-old boyfriend, who was in the back of the car with her, may have been the intended target.
Melanie’s father is related to Larry McCarthy Jr, a settled Traveller from Limerick who served a jail sentence in Britain for firearms.
Her boyfriend’s family is also related to the McCarthy-Dundon family.
Officers believe the attack may have been carried out by a criminal gang in Tallaght in revenge for the murder of a man in the area in 2009.
This gang suspect that a Traveller gang in the Brookfield/Fettercairn area was behind the 2009 murder, and Tuesday night’s attack may have been in retaliation.
Gardaí are investigating if a hitman from Ballyfermot, used by the criminal gang, was involved.
Detectives said this gang had been “lashing back” at the Traveller gang in recent months, including with pipe bomb attacks.
A respected drug activist in the area said there had been reports for some time that a Traveller gang was “going to war” against a rival gang.
This community worker said: “Guns are everywhere and gangs will resort to using them at the drop of a hat. The fabric of society that was there is gradually being eroded, which is being exacerbated by the removal of supports that were there for communities.”
There are reports that Melanie will be buried in the family grave in Limerick.
Her family described her as an “innocent child” who was in the wrong place at the wrong time.