You can actually accomplish this using the .concat method if you call it on an array of elements you want to put at the front of the new array.

Working Example:

var a = [1, 2, 3];
var b = [0].concat(a);
console.log(a);
console.log(b);

Alternately, in ECMAScript 6 you can use the spread operator.

Working Example (requires modern browser):

var a = [1, 2, 3]
var b = [0, ...a];
console.log(a);
console.log(b);

You can use:

var head = arr[0];
var tail = arr.slice(1);

Or in ES6:

const [head, ...tail] = arr;

You are looking for the ShiftRight method which is unavailable in the prototype. Here is a pollyfill:

Array.prototype.shiftRight = function(...params) {
   
    params.forEach(item => {
        for (var i = this.length - 1; i >= 0; i--) {
            if (i === 0)
               this[0] = item
            else
               this[i] = this[i - 1];
        }
    })
}


x = [1, 2, 3];

x.shiftRight(4, 5);

console.log(x);   // [5, 4, 1]

You can use the spread operator instead of unshift like this:

this.setState({
  todos: [
    {
      id: this.state.todos.length + 1,
      title: this.state.todoInput,
      done: false
    },
    ...this.state.todos
  ]
});

I'm not aware of any tools which allow you to figure out if the state is being mutated. But if you're up for using TypeScript you can declare the state as readonly to prevent this type of mutation.