Think about her personality and interests. If she would treasure the music box, that's a great idea. I love jewelry gifts but they do get lost, or never worn because they're treated as "too special to wear." Another option that isn't a keepsake, but will be a constant reminder of you, would be a membership for something she enjoys doing -- museum membership so you can visit once every six weeks or so and take her, and she can go with others at other times, or even a magazine subscription to something she would really be eager to receive each month.
Like others here, I'm concerned for you. You sound very loving but also very attached, and while attachment is good to a point, it might be getting in the way of your happiness as an adult here. Please, please go back and read Marda's wise post below and think it over with care. Can you step back from your emotions here and maybe try to look at your relationship with you undoubtedly dear niece as an outsider might see it? You are not, as Marda rightly says, responsible for her happiness, and you are not letting her down somehow by leaving -- you are building your own, adult life, with your husband to be. That's appropriate. Focus on doing that, and don't focus as much on how you will miss her. Be aware that your relationship with her will change and be ready for that change, so it doesn't cause you to damage your own marriage--that could happen, if you move and then are so invested in thinking about your niece that you aren't focusing on making a life in your new location with your new husband. He was handed a great job with hours that will allow you and him to see each other and truly be a couple -- that's wonderful! But you're seeing it now as "how could I tell him no?" That's troubling, because this is a good event that you're perceiving only or mostly in terms of how it affects your relationship with your niece.
If you were depressed last time you and she were separated (and it's good that you can see there were other factors, and it wasn't just her being away that depressed you), please take action BEFORE you marry and move. See a counselor or therapist and be sure that you are ready to embrace your marriage, this move, this job as totally positive. If you go into this new life clinging to her as she is now, at eight, by the time she's a bit older you're going to be hurt and confused when she naturally pulls away from you; you'll blame it on the move, on the marriage even, but it will be only because she's getting older and kids change and pull away from even the most loved and adored adults as they get older. It would happen even if you were still living close to her, but you might start to blame yourself, your move, your marriage, your husband's job. Stop that before it can even start and get an outsider like a counselor to see you before the marriage. You don't have to go forever, just enough to figure out why you're so invested that you feel so guilty about taking what is the best step for YOU.
Please update us here. I think it's lovely that you and she are close, please know that! You can stay close despite a few hours' distance, and sending her snail mail etc. is a great, fun way to do that. But I hope you can get past the guilt you're feeling, with some help. Enlist your fiancé to help too, and be sure you and he are communicating well and often about your feelings.