Enclosure would span 30 acres of land and create seven new full-time jobs, says application.
The incident happened in the Blaxton area of Doncaster in the early hours of Tuesday morning.
A planning inspector says a four-bedroom property can be built in a garden in Auckley.
Karl Mangham, 19, threatened to "shoot everyone" in the house before opening fire, police say.
Flocke, aged 12, and her three offspring are getting used to their new surroundings near Doncaster.
