DE isn't going to help at all, and you may cause respiratory irritation in your birds. I would not use it in the coop or out. In the US we use most commonly products that contain permethrin, both sprays and dusts to treat the birds and the coop. Spray tends to get in the nooks and crannies of the coop better. Elector PSP also works very well, but is much more expensive. Not sure what products you can get there, and am not familiar with Dr. Doom. In general you have to treat both the birds and the coop at least 3 times at weekly intervals, remove and replace all bedding and nesting materials each time (bag it up well or burn it). The chemicals kill the bugs, but don't kill the eggs, so the repeat treatments are necessary to get the ones that continue to hatch, so you kill them before they have time to lay more eggs. Otherwise, they will just keep coming back.
Good dustbathing areas are very helpful in prevention, I mix wood ash into my dustbath areas, just make sure it's only plain wood ash with no chemicals from paint or treatments to lumber, or other materials that could be toxic.
https://the-chicken-chick.com/poultry-lice-and-mites-identification/