Hola Marcos

We are using "I am having a dress made" with the same meaning as the other translation you suggest using "I am going to have...", I mean, we are still using this tense with a "future" meaning "I am having..." (not as a present continuous talking about a present situation, but as the future), the same way you can also say in English, for example:

I'm having a party {tomorrow].

She's leaving the country [soon].

We're making a booking at this hotel [this afternoon].

I hope this clarified it.

Saludos cordiales

Inma