Birds are going to have some arguments, that's just the nature of the beast. But it sounds like they like each other pretty well.
Jan is right though that it's MUCH too soon for a nestbox. The lutino is much too young for one thing, and they haven't been together long enough to form a pair bond which is VERY important to breeding success. They also haven't settled into their new home yet, and feeling safe and secure is also an important factor in breeding success.
But most important of all, breeding birds is a HUGE responsibility. There are about a million things that can go wrong and you have to be able to deal with any problems that arise. To do it right, you need to do a lot of reading on the subject in advance so you have a good understanding of what's involved, and make a realistic decision about whether you have the time, money and emotional strength to deal with any disasters that may occur (because disasters do occur all too frequently).
I'm primarily a cockatiel person so I don't know where to find the best resources on budgie breeding. But if you think you'd like to breed your birds later on when the time is right, I'd suggest reading this 10-part article on the responsible breeding of cockatiels to get an idea of what's involved. The issues might not be exactly the same as budgie breeding but it's probably not too different either. The different parts of the article aren't conveniently linked together so the navigation is a little awkward. Go to
http://www.birdsnways.com/birds/artspctl.htm#Cockatiels and scroll down to the R's and start with part one. Part 9 (IX) is listed out of sequence so watch out for that.