Can Somebody Tell what's wrong with my 1965 Mustang.?
Your engine has carburetor, one of the components of a carburetor are idle jets. They are what controls the amount of fuel that the engine gets at idle but if they're partially or fully clogged the results are similar to the symptoms you describe. How long since the carb has been cleaned? Once you accelerate, the main jets are controlling the fuel so there's no issue at speed, only at idle. There could be other reasons also but I'd start with the idle jets if the carb hasn't been cleaned in a long time.
Additionally, check the fuel pump to be sure you're getting fuel pressure, yours is mechanical, mounted on the engine block, not electrical. Check also the fuel filter if equipped.