Lots of hunter posts. Here is a true QOL hunter change.

[Sofaking]

2x the exp for pet level. This will give you a chance to tame new pets and easing the pain that is leveling it up.

Tamed a lvl 37 today as 44, couple of hours later of killquests, Im 46 while my pet is 38.

Had warmode xp buff and was rested, still crazy that the pet is actively falling behind while I do the most to making it catch up.

[Raukodor]

You already said the answer

You have warmode xp buff and rest buff. Pet doesnt

I play in turtle mode slow and steady and glyph of exhaustion. In my way till level 60 i have 2 pets and they are always in my level. With those exp debuffs pets levels up at same level than me (remember in slow and steady you lose exp on death)

[Striderbrah]

that's a warmode exp boost problem, not a hunter problem