Well, I like your enthusiasm. Just be aware that Doom was originally programmed in C with some assembly bits. Even if you wanted to do the whole thing in assembly, I’m not sure Processing is the best way to learn how to do that.
Programming a game rendering engine in assembly as a learner project is going to be pretty thankless, especially if you want output like Quake. It may be less like “building a house out of LEGO” and more like “using only silverware as tools to build a house.” Possible, but a miserable experience that may not produce an impressive end product.
If all-assembly rendering is your passion, I’d suggest focusing on learning it directly, not simulating it in Java. But ultimately it is up to you!