Hi,
I have installed nQuake which works awesomely with the original Quake, but I was wondering if it was possible to use it with the Quake Mission Packs also (Dissolution of Eternity and Scourge of Armageddon), and how do I do this?
Thanks.

As far as i know it isnt really possible, ezquake (the engine nQuake uses) is only for quakeworld while the quake mission packs, along with most mods are made for just vanilla quake.
If you want to play singleplayer stuff its recommended to use an engine like Quakespasm Spiked, also get the music to work with this guide

Thanks zigg, but when I went to download Quakespasm Spiked my antivirus flagged it as likely to contain viruses and warned me against proceeding! Any idea why that might be?

Likely a false positive as you're downloading .dll and .exe files, but you're welcome to check the source linked here https://github.com/Shpoike/Quakespasm
You would likely get the same warning downloading other source ports, ive been using QSS without issue for a while now so its definitely safe.