"Jeg vil ha en oransje kjole."

'ha' is part of the infinitive tense 'å ha', which is used after a modal verb such as 'kan', 'vil', 'må', etc...

'har' is the present tense.

It will be discussed in a later topic.

I think your sentence can be used but it may depend upon the intention of your question. By this I mean if you are asking 'Am I allowed to have an orange dress?' or 'Do I have the option of having an orange dress?' I think your sentence may work with my first sentence whereas, I think the second would be 'Kan jeg få en oransje kjole'.

I am learning norsk so I may be way off with my suggestion and understanding but hopefully it may point you in the right direction to satisfy your curiosity.

Lykke til!

"an orange dress" would have been accepted.

You use the indefinite article "a" before nouns that begin with a consonant sound, and "an" before nouns that begin with a vowel sound.