There have been many threads here about expensive audio gear in the context of relationships. Unfortunately they tend to degenerate into questionable advice and stereotypes.
First off, you shouldn't assume she's incapable of ever understanding. If you begin with this assumption communication is going to be a non option from the get go, and communication is an important facet of a successful relationship. I've spoken with audiophiles and have read plenty of comments in the past where the situation is treaded like a game of deception and one-upsmanship, basically expending time and effort to pull the wool over their eyes. In these cases the partner in question often has a conniption fit, and it has less to do with money in and of itself and more to do with the fact that a large purchase wasn't discussed before hand.
Let's be honest here: a 1000 USD pair of headphones is pretty unusual by most peoples' standards. A 500 USD pair of headphones is pretty unusual by most peoples' standards.
Maybe you can convince her it's worth its steep price tag as a piece of equipment. Maybe you can't. However you may very well have more success in convincing her it's part of your hobby and something from which you derive a lot of enjoyment. Try to explain to her why you enjoy these types of things. Explain to her that you hear a difference between one headphone and another. Even if she doesn't feel the same way or "get it" from a hobbyist's standpoint, she may feel more at ease if you involve her in the process. Suggest that you two listen together to her favorite music once you get the new headphones. Just keep in mind that this stuff takes patience: you shouldn't very well expect to throw headphones on someone with no experience and have them appreciate the improvements in sound right away.
Even if she can't hear what all the fuss is about, she should at least enjoy spending the time with you and being involved in your interests. In that sense you're not convincing her of the value of headphones, but rather the value of your headphone hobby. Establishing boundaries is crucial, and as an adult she should realize you have your own interests as she has hers. Even so, keeping the channel of communication open is important,