Congratulations on your wedding!
Although I haven't stayed at the places suggested by QF Lad, I have looked at some of them and they seem good.
I'm pretty sure all of them can be booked for under £300 per night - north QLD is not the most expensive place.
I suggest you try to stay in Port Douglas or if not in Palm Cove as these places are much more romantic than Cairns
I can definitely vouch for that comment. Port Douglas has quite a few decent eating places too, in case you get bored with hotel food.