Rather than tossing around semi-obsolete arts that aren't hers to give, Ling Qi might try furnishing Gu Xiulan with a more appropriately Ling Qi parting gift. More than most things, she is a musician. Ling Qi could grab that Bao guy to record a piece in jade to give to her friend. Three protests immediately leap to your lips, obviously. Ling Qi is uncomfortable with the notion of immortalizing her Music outside her self, Gu Xiulan has proven herself an... inattentive audience in the past, and what's a song supposed to accomplish in any case? Let's look at why those concerns are not an obstacle to a musical gift.
First off, it's precisely because Ling Qi has reservations that the gift would be especially meaningful. Pushing her own boundaries for her loved ones is also slap dab in the middle of her SCS insight and broader family focused Way. And it's not like it's a sacrifice she'd be making, just something she's a bit uncomfortable with but that doesn't harm or diminish her in any way. On a meta level, it'd also be nice to see Bao roped into focus and give him pretty stark exposure to Ling Qi's inner character.
Secondly, it is obvious that Xiulan would pay no attention to songs on such pedestrian matters as sightseeing among mountains; that's more the speed of someone like Shen Hu. Playing to this audience requires a more impressive subject: Gu Xiulan. Fortunately, Ling Qi has pretty close knowledge of that subject, and has been around for many of her feats and trials, not least of which is the fiery girls recent stand against wave after wave of impure spirits while astride a legendary beast. There's a lot to work with, and Xiulan's naturally inclined to appreciate the subject matter.
Lastly, most importantly, what's the point anyway? Well, foremost the point of a heartfelt gift is, uh, giving a nice thing to a person? Doesn't need to be more to it than that. But if that doesn't cut it for you, consider that the message of the song would be sincerely heartfelt by definition of the medium and from a person she truly trusts. And also Ling Qi isn't a jerk. Consider what we know of Xiulan's upbringing; a sincere and uncritical "Yer awesome, bro" from someone she respects isn't something I'm sure she's had before. We'd be just handing her a permanent one she can keep in her pocket. Of course, just because it's honest and not critical doesn't mean it can't challenge her or make suggestions to her in other ways. If the melody extends into the future, there's material Ling Qi can draw on. Yanmei's fires, the scale and awesome presence of the prism dragon's power, the efficacy of her steadfast flames when bolstered by Zhengui's Wooden backing.... (Hint hint) Heck, Ling Qi could even slip in some rueful acknowledgement of Xiulan's very successful team up with the growing boy, assuming poking her twoards Wood is something Ling Qi actually thinks might be productive.
In any case, I'd rather be leaving Xiulan with something that comes from Ling Qi's heart than something she happens to have on hand anyway.