I have seen many posts indicating the need for a GPU like the RTX 3090 to convert a native 1920 x 1080 clip. I will say that, my PC has an i7-9700k, 32 GB RAM, and an RTX 2070 Super with 8GB VRAM. The first time I tried to convert a 1 minute 1080 clip, I DID get the out of memory error. But then, instead of reducing the size, I monitored the task manager to see how much of the (dedicated) VRAM was actually being used. At any given time, the MAX amount being used by DAIN was 6.8 GB. However, I had other programs open in the background such as Topaz Video Enhance AI (sitting idle, not converting anything. and no video loaded into it) and Chrome playing a YouTube Video. I then closed Topaz, Chrome, and actually anything else so that the only program running (not counting system apps) was DAIN. I was THEN able to convert that 1080 video clip without having to scale it down to 1820 x 720. In other words, close other apps that may be utilizing the GPU and as long as you have at LEAST 8 GB VRAM, you SHOULD be able to convert WITHOUT down scaling the resolution.
It worked for me, so perhaps it will work for you as well. :)