Is this considered an acceptable ghusl?

I had the intention of making ghusl by going under the shower, washing my hair first with shampoo then washing it off. Then washing the top part (front and back) of my body with soap and water, and then washing my private parts with soap and water, then washing the bottom part (front and back) of my body with soap and water. I then rinse my mouth 3 times and my nose 3 times. Is this considered acceptable ghusl? (I am a woman if that makes any difference).