The Tamil family fighting for Australia's protection will remain in detention on Christmas Island until February when their case will go to a full and final hearing in the Federal Court.

Parents Priya and Nadesalingam and their Australian-born daughters Kopika, 4, and Tharunicaa, 2, will spend summer on Christmas Island, where they have been since August, before their fate is finally decided in court.

Federal Court Justice Mark Moshinsky will hear the case over two days on February 21 and 25, after which they could be immediately deported back to Sri Lanka.

Tharunicaa, left, is pictured with her four-year-old sister Kopika. Credit:AAP

The trial dates were set on Thursday after a succession of court injunctions stopped government attempts to deport them.