I am aware of that specific attack pattern, but I've had her go invincible whilst in other patterns as well. It's similar to when you exit the biome you summoned her in, or when she has Guardians out, but neither of those are true, nor is she in her chrysalis-looking mode that you're talking about.
One thing I should have mentioned when I was talking about the DoG was that I was using the Andas Core jetpack/wings(?) from the Tremor mod to fight the boss, which allow for indefinite, relatively fast flight. The main issue I was having with the lasers is that whilst using wings, you must be moving either up or down in addition to whatever horizontal direction you're moving (unless you manage to mash spacebar at just the right interval to keep level, which I've never seen anyone pull off, to my knowledge). Since you're always moving slightly up or down, when Doggo fire's it's horizontal lasers, the only possible way you're gonna avoid hitting them (especially at the velocity it takes to outrun the boss) is with sheer luck, or if your game is lagging so hard that you're in bullet time for the whole fight.
Also, do you mean spamming dash in the direction you're kiting the boss? At any rate, I don't even have a free accessory slot that I could put a counter scarf, since I'm stacked up on offensive accessories to kill bosses before they even get the chance to pull any of their shenanigans (seriously, if the Ceaseless Void or Polterghast had any fancy tricks they used as their health went down, my Telluric Glare didn't let them live long enough to see them). I would suggest potentially adding the Counter Scarf to the recipe for the Seraph Treads, since they already serve as a sort of panacea (Mastaaa used Big Words! It's not very effective...) in terms of mobility accessories. Having to use an accessory that drops from Big Bumbo Dumbo Eye at the Beginning of the Game to fight the Almighty Unraveller of Multiverses and Consumer of All Powerful Individuals seems really, really silly.