I've got a lot of pets that I'm leveling for sale so they're all named 'Nameless' because I've found people also like naming their critters on their own. 

The problem is, I don't know which Nameless I'm working with!  So, I merrily pop onto an Island, run them around, and begin fighting the monsters, and I go "Oh!  A level 6 monster!  No problem!" Then promptly lose to it, because the Nameless i'm working with is level 3.

It'd be awesome if it could say in the upper right:

Active Pet: Nameless (lvl 3) (Energy: 6)

That would be useful. All of my pets are named because Nameless bugs me but I still forget the correct level for my pet.

I've got in the habit of exploring the island as fully as I can before I start fighting mosters. Then I start fighting the lower level mosters, explore the new area revealed, and continue working my way up through the higher leveled mosnters, leaving the the red and pink guardian monsters to last (and any bosses until after all the guardians are beaten) It seems to help but it takes longer because I'm weaving back and forth over the map. If the level was displayed I could blast through the monsters that are several levels below mine

Yesyesyes! Even though I name most of my pets, I still forget level occationally, or don't see that the pet has  leveled up while exploring.

This has already been suggested in various forms before, either in the form of a information list that could dock on the side of the explore window, or as you said near the pet name. It'd been brought up a number of times and has always recieved overwhelming support.

Though, the developers of this game have a lot of things to do, add, improve, balance, etc. So I'm positive that it's on the to-do list. Just be patient and I'm sure it will get added eventually.

I check two pages back before I make a suggestion.  I didn't see it, so I thought I'd suggest it.

Maybe, another suggestion would be an ongoing list of all suggestions? 

*adds her own support* i dont tend to have many nameless, but i do have a lot of pets, and dont remember what levels they all are