Rise in AD increases Y as per AS-AD model.
The Aggregate demand curve AD, which is downward sloping, is derived from the IS – LM model.
It shows the combinations of the price level and level of the output at which the goods and assets markets are simultaneously in equilibrium.
Since goods market is in equilibrium and that too for higher demand, then prices mist have increased.
I believe, AD curve is post- equilibrium condition , so pre-equilibrium conditions are of no significance.
If aggregate Demand increases and if the aggregate supply of goods can also increase then the real GDP increases as this leads to increase in production. Naturally the real GDP goes up and the price will not increases as there is an increase in the supply to match the aggregate Demand