Per the Pathfinder Roleplaing Game Conversion Guide, you can just convert the battlerager class directly.
In the case of the battlerager, it’s pretty simple:
The requirement for Intimidate should be only 5 ranks, instead of 8, because of Pathfinder’s changes to skill rank maximums.
The extra daily uses of rage should be converted into daily rounds of rage. The 3.5 barbarian got an extra daily use of rage every 4 levels, while the battlerager gets one every 2 levels, effectively doubling the rate that the barbarian saw it. The Pathfinder barbarian gets 2 rounds of rage each level; the battlerager therefore should get 4 rounds each level.
Aside from those, everything else works in Pathfinder as well as it did in 3.5. BAB, alignment, race, and “ability to rage” haven’t changed, the Cleave, Endurance, Power Attack, Improved Unarmed Strike, and Great Cleave feats still exist, the concepts of skill bonuses, saving throw bonuses, natural armor, and immunities to various effects have not changed.
The feats Close-Quarters Fighting and Reckless Offense do not exist in Pathfinder, but they would work in Pathfinder no problems. You could either port them as feats, or you can just turn them into unique class features of the battlerager class.
I will comment that this class is problematic in that it does not let you learn new rage powers, and doesn’t even count towards your barbarian level for the purposes of learning new rage powers once you return to the barbarian class. This is, however, consistent with the 3.5 battlerager, which didn’t help you get Greater Rage et al.. The above port of the battlerager is very consistent with the 3.5 one, but the 3.5 battlerager was a very weak class.
The more “Pathfinder-ish” approach here would be to give dwarves a racial barbarian archetype. Say, trading Trap Sense for Gruff at 3rd, Rock Gut at 6th, Close-Quarters Fighting at 9th, Fearless at 12th, Reckless Offensive at 15th, and Natural Armor at 18th. Spreads those features out over more levels, and doesn’t offer Improved Unarmed Strike or Cleave as bonus feats, but you get all of your rage powers without missing any.