Problems with AsyncTask

I'm trying to make a request for JSON along with AsyncTask. With this, I made the JSON call in the InBackground method, however, the code executes the onResponse method of the JsonArrayRequest after calling the onPostExecute, not at the time of its due call.

public class MainActivity extends AppCompatActivity {

    private TextView tvCarregandoLogin;
    private GifTextView gifLogin;

    private String resposta = "";

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.lay_login);

        tvCarregandoLogin = (TextView)findViewById(R.id.tvCarregandoLogin);
        gifLogin = (GifTextView)findViewById(R.id.gifLogin);
        tvCarregandoLogin.setVisibility(View.INVISIBLE);
        gifLogin.setVisibility(View.INVISIBLE);

        new GetTask().execute();
    }

    class GetTask extends AsyncTask<Object, Void, String> {
        @Override
        protected void onPreExecute() {
            super.onPreExecute();

            gifLogin.setVisibility(View.VISIBLE);
            tvCarregandoLogin.setVisibility(View.VISIBLE);
        }

        @Override
        protected String doInBackground(Object... params) {

            JsonArrayRequest jsonArrayRequest = new JsonArrayRequest(Request.Method.POST, Auxiliar.json_url_getEspecialidades, (String)null, new Response.Listener<JSONArray>() {
                @Override
                public void onResponse(JSONArray response) {
                    String descricao = "";

                    for(int i=0; i<response.length(); i++)
                    {
                        try {
                            JSONObject jsonObject = response.getJSONObject(i);

                            descricao = jsonObject.getString("Especialidade");
                            resposta += descricao + "~";

                        } catch (JSONException e) {
                            e.printStackTrace();
                        }
                    }

                    onEspecialidadeIsReady(resposta);
                }
            }, new Response.ErrorListener() {
                @Override
                public void onErrorResponse(VolleyError error) {
                    Toast.makeText(MainActivity.this, error.toString(), Toast.LENGTH_LONG).show();
                }
            });
            MySingleton.getInstance(MainActivity.this).addToRequest(jsonArrayRequest);

            return null;
        }

        @Override
        protected void onPostExecute(String result) {
            super.onPostExecute(result);

            gifLogin.setVisibility(View.INVISIBLE);
            tvCarregandoLogin.setVisibility(View.INVISIBLE);

            //fazer alguma coisa com a variavel resposta
        }
    }

    public void onEspecialidadeIsReady(String r)
    {
        resposta = r;
    }
}

MySingleton Class

public class MySingleton {

    private static MySingleton mInstance;
    private RequestQueue requestQueue;
    private static Context mCtx;

    private MySingleton(Context context)
    {
        mCtx = context;
        requestQueue = getRequest();
    }

    public RequestQueue getRequest()
    {
        if(requestQueue == null)
        {
            requestQueue = Volley.newRequestQueue(mCtx.getApplicationContext());
        }
        return requestQueue;
    }

    public static synchronized MySingleton getInstance(Context context)
    {
        if(mInstance == null)
        {
            mInstance = new MySingleton(context);
        }
        return mInstance;
    }

    public<T> void addToRequest(Request<T> request)
    {
        requestQueue.add(request);
    }
}