Based on dialogue in that final story, the series most likely was intended to feature Rose's life on the alternate Earth the Doctor had dubbed "Pete's World", working with that reality's version of the Torchwood Institute.
The series had been commissioned by BBC One but abruptly cancelled by Russell T Davies, who decided that it would have lessened the impact of Doomsday. The spin-off was cancelled before Billie Piper had been formally approached. Reportedly the original plan was to produce a one-off special (likely for broadcast around a holiday, possibly Easter), followed by more specials if demand warranted, in lieu of a weekly series.
Piper agreed to return as Rose in the 2008 season; after a trio of surprise cameo appearances earlier in the season, Piper appeared in the finale trilogy of Turn Left, The Stolen Earth and Journey's End. In these episodes she is shown communicating with an unidentified support team and at one point also takes command of a group of UNIT soldiers in the parallel Earth of Turn Left. It is not known if any of this connects with elements of the aborted Earth Defence series concept.
The name 'Rose Tyler: Earth Defence' was inspired by the Doctor's meeting with Rose in Doomsday. Rose says that she plans to join the Torchwood Institute of Pete's World. The Tenth Doctor smiles and replies Rose Tyler, Defender of the Earth.