It is not possible to refer to item id nor a property from inside TextItem.cursorDelegate:

    property color cursorColor: "blue"
...
        TextInput {
            id: textInput
            anchors.fill: parent
            cursorDelegate: Cursor { editor: textInput; color: cursorColor }
        }

When trying to do so you'll get errors like:

ReferenceError: Can't find variable: textInput
ReferenceError: Can't find variable: cursorColor

Similar code works for TextEdit, however.

Full example attached.