XPS 13 9360, only FHD on external QHD monitor

You don't need special Dell docks or adapters to use higher resolution, because the maximum resolution available depends on the system's hardware and how you connect everything.  When using a Thunderbolt device rather than just a regular USB-C device, that system can handle dual 4K 60 Hz displays out of that port and even some triple display configurations.  A conventional USB-C to DisplayPort cable when connected directly to the system, i.e. not through any other dongle, dock, adapter, etc., would be able to handle a single 4K 60 Hz display.  And regular USB-C (non-Thunderbolt) adapters that offer both video output and other functions like USB ports, Ethernet, etc. would still be able to support at least a single QHD display or 4K 30 Hz.  Some of those adapters like the Dell DA300 can technically support 4K 60 Hz even over regular USB-C, but that's only possible when the system itself supports DisplayPort 1.3 or better, but the XPS systems only support DisplayPort 1.2 because no Intel GPUs currently on the market support anything newer.  That will change with the "Ice Lake" CPU family slated for the end of the year, though.

Since you didn't link the specific Thunderbolt to HDMI adapter you're using, I can't say much about that, but the USB-C to DisplayPort cable should absolutely be working.  I personally use a USB-C to DisplayPort cable with an older XPS 13 9350.to run dual QHD displays (via DisplayPort daisy-chaining).  If you're using that type of cable and it's connected directly to the system, I'm not sure what's going on.  I guess try updating your system BIOS/firmware and Intel Graphics drivers if you haven't already.  Otherwise, do you have another system you can test that display and cable with (or at least the display's DisplayPort input with), or else another higher resolution display you can test your system and cable with?

Side note: I know that you specified 1440p as well, but fyi "2K resolution" as you specified in your thread title is a dangerous thing to say because so many people use it incorrectly -- including you in this case -- and sometimes the difference can matter for technical reasons, including situations like this where different connectivity setups allow different amounts of display bandwidth. 2K resolution is technically a film resolution of 2048x1080, but when used to refer to "consumer" resolutions, it actually refers to the nearest and slightly lower consumer equivalent, which is 1920x1080, aka Full HD or 1080p -- because 1920 is very close to 2000, i.e. 2K, horizontal pixels. Similarly, 4K is also technically a film resolution of 4096x2160 pixels, but when used in the consumer world refers to the slightly lower resolution of 3840x2160, aka Ultra HD or 2160p. The resolution you have is rightfully called 1440p or QHD (or I guess you could call it 2.5K, but nobody does), and using either of those terms would make it much clearer to everyone what you're talking about.