put me on a dress, put a dress on me?

She might say, “Dress me, please.” This is quite formal and might be said to a Nanny.
More likely, she can say, “Put me in a dress, please.” This implies she sometimes prefers play clothes that may be allowed for rolling on the ground.
Or she can say, “Put a dress on me, please.” This is equal to the previous suggestion.

I want to make sure that you understand that a "dress" is only one type of clothing item. We can "get dressed" in any type of clothing, not just dresses.

If she just wants help getting her clothes on, she can say "Please help me get dressed."

If she says "please put a dress on me" she specifically wants to wear a dress, not shorts or jeans or anything else.

Thank you...

If she says " put this clothes on me",

Would this sounds natural?

Thank you again..

If she says, "Put these clothes on me", she is asking to be dressed in some clothes she has identified.
As indicated earlier, it will depend on how old a girl she is. The assumption is that she is unable to dress herself.

Thank you so much~!!!