I posted Sorting QML ListModels on GeoNet AppStudio Blog Posts.

    function listModelSort(listModel, compareFunction) {
        let indexes = [ ...Array(listModel.count).keys() ]
        indexes.sort( (a, b) => compareFunction( listModel.get(a), listModel.get(b) ) )
        let sorted = 0
        while ( sorted < indexes.length && sorted === indexes[sorted] ) sorted++
        if ( sorted === indexes.length ) return
        for ( let i = sorted; i < indexes.length; i++ ) {
            listModel.move( indexes[i], listModel.count - 1, 1 )
            listModel.insert( indexes[i], { } )
        }
        listModel.remove( sorted, indexes.length - sorted )
    }