I just tested and was able to get it to not only load, but produce a working quarry in 0.18.44, it takes a little effort to fix it but not too much. The steps to do so are listed below:
1: Unzip the file to extract the folder
2: Go into the folder and open info.json using wordpad (notepad or any other text editor probably works too)
3: Scroll down to the line which reads "factorio_version": "0.17",
4: Replace the 0.17 with 0.18
5: Save the file
6: Re-zip the folder and replace the original zip file with the new one
7: Start the game up, load the mod like usual, play as you desire
This works because there aren't any actual dependencies missing from the Quarry mod in 0.18, no animation files have been renamed, nothing has been changed, it's just set to only work with version 0.17, so just changing that to say 0.18 will let it work fine. Since the 1.0 patch release is coming up soon, and it's been set to work with any 0.18 mods so that they don't have a big mess on release day, you'll just have to go in and repeat this process again when 1.0 is released and it should still work without any issues.
This may not work with other mods, but I can confirm it at least allows you to load and build T1 quarries. I haven't tested the T2 and T3 quarries yet since I just started a new game to test it out, so there's the potential for there to be an issue there, but it's probably fine.
So yeah, enjoy having quarries working again! It was one of my favourite mods to use, so it was worth the little effort to get it back up and running again.
