Will the flight be delayed in dusty weather?

It does, but it depends on how big the dust is.

For an extreme example, on October 25th, 20 14, 10/0, there was a severe smog in Beijing, which caused many flights that arrived in Beijing that night to fail to land and fly to other airports. Aeroflot SU200 circled over Inner Mongolia for eight times and stayed in the air for one and a half hours, waiting for the arrival of the wind, until the cold air blew away the smog, and landed at Beijing Airport in the early morning of 26th.