"Hun vil ha et ekteskap og en familie."

Translation: She wants to have a marriage and a family.

[VideoDrome]

Is it common for someone to say "have a marriage" instead of "get married" or is there a verb for that?

[derpkins]

I put wedding and it didn't accept it. Are there seperate words for wedding and marriage?

[Kabaczek666]

Yup.
ekteskap = marriage; bryllup = wedding.

[Athalawulfaz]

I put "She wants to have marriage" and was marked wrong, yet this feels much more natural in English than "a marriage", despite the use of the indefinite article in Norwegian.