A few nights ago, I was getting ready to heal Gundrak (for which one should always have a hunter) with a group of very friendly people, and we were chatting away while waiting for people to make their way to the stone. We were on the topic of PuGs in general, and the level 77 hunter in the group lamented having been booted from a PuG earlier that day for having a level 76 pet, rather than a level 77 pet.
While we didn't hear the other players' side of the story, it struck me as odd to go so far as to boot someone from a non-heroic, 5-man instance for having a pet one level lower than himself. Now, it takes a whole lot to convince me that someone needs a boot in general, but even so... Trying to see this from the other side, I can only guess that the party leader must have been familiar with the importance of having level 80 pets in heroics and raids, and must have applied the same sensibility to his leveling party.
It's a fact of leveling that your pet will spend the first 20% or so of your next level being one behind, but if you're doing non-heroic instances your own level, this shouldn't be an issue. This isn't to say that pet levels don't matter. They do. They matter a lot. The difference between a level 79 pet and a level 80 pet is huge. The difference between a level 78 pet and a level 79 pet, on the other hand, is fairly minimal. Allow me to illustrate:

Chance-to-hit
In a raid setting, it's imperative that pets be max level. In heroics, pets really ought to be max level, but if the group is okay with a hunter knocking out that last level, and you can absorb the DPS loss, a level 79 pet is alright. 78 is pushing it. For regular instances, it's nice if the pets are their master's level, but it shouldn't really be an issue if the pet in question is the one the hunter has been leveling with, since it should never be but a level behind the hunter.
Why the difference? In part, it's the mobs you're facing off against - a level 78 pet is going to miss heroic Keristraza's big, red, level 82 hide a whole lot more often than a level 80 pet will. The same goes for any pet four levels below the mob it's attacking. Missing 15% of your attacks is missing 15% of your DPS. If your pet is ~40% of your total DPS, that's 6% of your DPS down the tubes. Ick.
Trash mobs in raids are levels 81 - 82 and bosses are 83. In heroics, trash mobs are 80 - 81 and bosses are 82. In regular, level 80 instances, trash mobs are level 79 - 80, and bosses are 81. So, the hit cap for a level 80 instance is 5.2%, or 165 hit rating. If your pet is one level below you, his hit cap against a level 81 mob is 5.4%. Problem though: pets only inherit full percentages of hit from their masters and Focused Aim does not apply to pets. So, unless you're astonishingly well-geared for having just hit 80, and you have 197 hit rating (granting 6% hit), there's very little difference from your pet's perspective. In fact, there is a .2% chance-to-hit difference. If you're Beast Mastery, the expertise from Animal Handler should go a long way toward limiting the other worrisome factors of glancing blows and parries.
This can be applied to lower-level instances as well. Boss mobs are usually one level above the instance level, meaning you and Fluffy have about a little more than a 5% chance to miss them, regardless of whether he's your level or one behind.
Pet Skills
The other important factor is pet skill ranks.
Just like us, hunter pets learn new skills and new skill ranks as they gain levels, with the last set of skills being learned at level 80. Unlike us, though, they do not gain new ranks of one skill or another every level, or even every other level. Take Cats, for instance. A new rank of Claw is learned every eight levels, while a new rank of Rake is only learned every sixteen levels!
This holds true for all of the pet family skills. Each family (such as Bears, Ravagers, Crabs, etc) has two skills.* The first is a DPS skill, while the second is either a DoT or a utility skill, depending on the family. The DPS skill gains a new rank every eight levels, while the second skill gains one every sixteen levels.
For a Ferocity pet, these special attacks comprise about 40% of overall DPS, so those shiny new ranks are a big boost. The last ranks of both abilities are learned at level 80. Between 72 and 79, however, the pet learns nothing new. The only difference will be the relative levels and base stat improvements. These are nice improvements, of course, but handing Fluffy a sack of Spiced Mammoth Treats would go a long way, too.
Of course, if you're doing Halls of Lightning at level 76, well, that's a whole 'nother can of worms.
*Cats and Spirit Beasts are special. These families have Prowl, as well, which ranks at levels 30 and 50. Spiders, Tallstriders, Warp Stalkers, and Tutles are exceptions to the sixteen level rule, as their utility skills, Web, Dust Cloud, Warp, and Shell Shield, have only one rank.

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