Keep in mind that in order to get this option to show up, you’ll need a phone that supports such high resolutions, like an LG G3 or an Oppo Find 7. It’s also important to note that the video in question will need to support the resolution. Even if you have a device that supports the resolution and a video that should work with it as well, don’t be too surprised if you don’t see the 1440p option.
Reading various blogs and forum posts around the web, it seems that some folks are having luck with finding the 1440p option, while others aren’t. This isn’t too shocking, considering Youtube tends to have issues when it comes to recognizing and matching resolutions, as evidenced by the fact my Nexus 5 doesn’t allow anything higher than 720p.
Another reason why the 1440p option might not show up for all QHD-equipped handsets is that Google could simply be testing things out, and therefore rolling it out slowly to users at random. Either way, it’s only a matter of time before your LG G3 (or any QHD mobile device) can watch above-1080p resolutions right from the Youtube app.