Establezca el inicio del campo Incremento automático desde 1000 en laravel de migración 5.1

Debería ser así (no probado).

use Illuminate\Database\Migrations\Migration;
use Illuminate\Support\Facades\DB;

class MyTableMigration extends Migration {

     /**
     * Run the migrations.
     *
     * @return void
     */
    public function up()
    {
        $statement = "ALTER TABLE MY_TABLE AUTO_INCREMENT = 111111;";
        DB::unprepared($statement);
    }

    /**
    * Reverse the migrations.
    *
    * @return void
    */
    public function down()
    {
    }
}

Actualizar

//Your migrations here:
Schema::create('users', function (Blueprint $table) {
    $table->bigIncrements('id')->unsigned();
    $table->integer('qualification_id')->nullable();
    $table->integer('experience_id')->nullable();
});

//then set autoincrement to 1000
//after creating the table
DB::update("ALTER TABLE users AUTO_INCREMENT = 1000;");