var myobject = new MyClass1("5678999", "text");
var dto = { MyClass1: myobject };
console.log(JSON.stringify(dto));
EDIT:
JSON.stringify will stringify all ‘properties’ of your class. If you want to persist only some of them, you can specify them individually like this:
var dto = { MyClass1: {
property1: myobject.property1,
property2: myobject.property2
}};