All lowbie brutes have end issues. Attacks use more end than toggles, so yes you slot them for end reduction. Do you have SOs yet (has 20 ish got to 22 yet) ? if not it will improve when you get SOs in stamina.
There are some good guides to endurance dysfunction focussed on brutes, but most recommend slotting for acc and end not damage pre SOs.
Your ultimate aim is to hit the defence softcap (45%) to all positions, so use sets that help you to achieve that, plus the steadfast protection res/def.
It's true. This game is NOT rocket surgery. - BillZBubba
At the beginning levels its a good idea to slot EndRed rather than Dam in Brutes attacks and let Fury do the damage.
Later on in life sets such as Touch of Death and Mako's Bite will increase your Melee and Ranged Def by 3.75% respectively with 6 slots.
Scirocco's/Eradication (PBAOE) provides 3.75%/3.13% AoE Def at 6 slots (I THINK those are the values?) plus some other good set bonuses (LOVE the Erad's +2.25% Max HP at 4 slots).
Obliteration gives +3.75% Melee Def at 6 slots but can be difficult to find on the Markets and is quite expensive.
Put a full set (6) of Gaussian's in Build-Up for another 2.5% Def (all Pos).
Combat Jumping will also help while leveling and you may be able to respec out of it when you get higher levels and more IO set bonuses if you want to. Even if you have reached the s/c for all positions CJ can be used as a mule to hold a LotG +Rech, Kismet +Acc, etc.
And of course Weave 
.
Like Minotaur said SO's will make a HUGE difference when you get them.
With Alignment Merits obtainable solo from level 20 you can start building up your collection now to get the sets as needed.
Depending on how often you play this toon you can realistically get 2 AMerits a week (you can get more if you play more of course).
The Healing Uniques (Numina, Miracle, Regen Tissue) all cost 2 AMerits so thats a weeks worth of Tip Missions per Unique.
The Steadfast Res/+3% Def that Minotaur mentioned can be slotted at any time (the Res component is low anyway).
The Eradication sets caps at level 30 so once you get to level 27 - slot up.
Once I have SO's I normally slot 1x EndRed & 3x Def in my main Def Toggles (Deflection + Battle Agility).
/5cents
Okay, I'm thinking about my Axe/Shield brute fresh out of Praetoria. And what exactly to do with him. (so he's around level 20-ish currently)
1. I have endurance issues. even with fully slotted Stamina. Should I just bite the bullet and slot endredux in my attacks?
2. Axe seems to do very nice burst damage with some control, but as said, endurance is an issue. Any slotting suggestions? (IO sets etc?) Seems to have relatively few options for slotting in attacks (PBAOE, Melee Attacks and Knock sets seems to be it)
3. Overall my main issue seems to be endurance (the same as with my SS/Inv brute in fact) just using stamina doesen't seem to cut it.
4. Any skippable powers (although with Inherent Stamina i'm more likely to run out of slots)
"Men strunt �r strunt och snus �r snus
om ock i gyllne dosor.
Och rosor i ett sprucket krus
�r st�ndigt alltid rosor."