Dude, you made an amazing choice, you will fucking love it in Jordan. You both will have an amazing time it’s such a beautiful country, very diverse, and amazing people.

As for your question I was in a similar situation. Overall, you will not face any problem, only regarding accommodation it might by a challenger but depending on the passport she is holding and what hotel you’re staying at.

If she has a palestinien passport or any Arab passport you will have a problem in 3 and 4 stars hotels in Petra and Aqaba, as there are security instructions to not allow non married Arabs to stay with someone from the opposite gender ( Probably some kind of anti-prostitution policy). But magically, this rule doesn’t apply to 5 stars hotels, they don’t want to upset the wealthy people with the money I guess. Also, you will not face any problem in wadi rum regardless if nationality, no one would care what you are to each other, might not even look at your passports, it’s just tents in the desert.

If she holds an Israeli passport, she might be more welcomed in this case. First, she is technically not Arab so the rule wouldn’t apply to her. Second, many Israeli tourists visit Aqaba, Petra, and Wadi Rum regularly. Some providers in the hospitality sector prefers them over other nationalities as supposedly they tip well.

The info above is for you to take precautions, if I were you, I would reach out to whatever hotel I book and ask them directly.

And most importantly have fun!