Rage on a subclass of a fighter or ranger is OP, my friend.
I dont think so, no. We talking of a 1 minute effect per short rest?
But I'd go for a refluffed Reckless attack to represent Rage.
Berserker (Fighter)
3:
Rage
You can throw aside all concern for defense to attack with fierce desperation. When you make your first attack on your turn, you can decide to attack recklessly. Doing so gives you advantage on melee weapon attack rolls using Strength during this turn and you can add your Constitution modifier to the damage roll, but attack rolls against you have advantage until your next turn.
3:
Great Might
You have advantage on STR check. When you grapple a creature, it is also restrained.
7:
Berserker's Vitality
When you use Rage, you also gain temporary hit points equal to your 1d8+ Constitution modifier (minimum of 1).
10:
Mindless Rage
You can't be charmed or frightened until the start of your next turn if you use Rage. If you are charmed or frightened when you enter you use Rage, the effect is suspended for the duration of the rage.
15:
Frenzy
If you take the Attack action on your turn and have advantage on an attack roll against one of the targets, you can forgo the advantage for that roll to make an additional weapon attack against that target, as part of the same action. You can do so no more than once per turn.
18:
Strength Before Death
If you take damage that reduces you to 0 hit points and doesn't kill you outright, you can use your reaction to delay falling unconscious, and you can immediately take an extra turn, interrupting the current turn. While you have 0 hit points during that extra turn, taking damage causes death saving throw failures as normal, and three death saving throw failures can still kill you. When the extra turn ends, you fall unconscious if you still have 0 hit points.
Once you use this feature, you can't use it again until you finish a long rest.