Legally, it doesn’t matter whether you’re doing it for public performance, private use, for money, or for fun.
If the end result is to end up with two separate copies that two people can use separately in the same way as two purchased copies could be used, then it is probably not fair use.
If you are both reading off the same copy or taking turns taking the music home to practise individually, there has been no “unauthorized copying,” and therefore no copyright violation. The key is in the copying.
If you are talking about an ensemble in which each performer will be reading off a separate copy, either during the performance or just in rehearsal, then you must purchase a copy for each performer. It is probably fair use for a performer to make a photocopy to mark up or to avoid damage to the original, but it is probably not fair use if the photocopy is being used to INCREASE the number of copies in use. It is probably not fair use for stand partners who are sharing music during the to make copies so that both can take music home without buying another copy.
In other words, if the orchestra has 12 first violins and 12 first violin parts have been legitimately purchased, then it is probably okay for each first violinist to make one copy of his or her sheet music to carry around and mark up, but if the orchestra decides that more violins are needed, and, say, for the sake of example, doubles the size of the section to 24, then those 12 photocopies cannot be used to pass out to the 12 new first violinists. Twelve new copies must be purchased (or legitimately acquired in some way – note that if your orchestra is renting music, then the rental contract will have provisions covering all these instances, some which will allow you to make photocopies yourself for certain purposes).
In the case of your duet, my guess is that making a copy for your partner to practise off of would not be considered fair use. Reading off the same music at the same time is okay. Taking turns passing the score back and forth to practise is okay. Neither of these is any problem, because you haven’t made any copies.
But, if you are using the copy in a way that is essentially replacing the purchase of another legitimate copy–in other words, you are both at your separate homes at the same time practising the music, one off the purchased copy and one off the photocopy–then it’s probably not fair use.