So just caught a Luffox but It's stats are kinda all even I thought I could use it for breeding so I wanted to buff the stats a bit by fight so the hatchlings would have better stats.
But I looked at the stats.
Strength: 41 (12 + 0)
Intelligence: 41 (12 + 0)
Dexterity: 39 (10 + 0)
Agility: 39 (10 + 0)

There nothing I can do for the stats because there is no option with Strength and Intelligence.
Maybe someone in the comments could find out what the Luffox's Element could be? :P
https://www.sylestia.com/view/pets/?petid=4496932

Increasing stats can only be done at the time an egg hatches, or by nurturing a hatchling many many times. Leveling it or assigning elemental traits will not increase its offsprings' stats, though I think it can increase their level by a small amount.

If you're interested in stat breeding, check in the Player Guides section of the forums. I believe there are some much more detailed explanations there.

I know just I wanted to level it up is what I meant

Well, it's already attuned to the Light element and has its proficiency point put into health, so all you need to do now is put it in your party and fight a lot until you reach a much higher level when you can assign a second proficiency point. Or send it on missions, if you don't want to fight.

I guess it would be a good idea to get some gear too, but I'm not the right person to help with that. I'm still kinda lost on what to equip pets with.

I have the perfect thread for both of you.Guide to battling here
There events part included with it...Also, purple Red and orange are really good equipment but really expensive when you start so I recommend to try to get rare gear...And don'tbut discipline gear on batthe (a.k.a party) pets.