IMHO I would learn Moose first. Why? Yes, most Perl OO is not done doing Moose. Yes, Moose is slow (though try Mouse). Yes, there's lots of practical reasons why you're going to have to eventually learn to do it the hard way. But there's one overriding reason.
Because Perl's way of doing OO warps your brain.
The point is to learn good OO, not Perl's OO. Once you understand OO programming as a concept them you can apply the technique to any specific language. The reverse is not so true.
Perl's stock OO doesn't give you much at all. You have to build all your pieces yourself. You have to learn all the little details of how everything works. It teaches you broken concepts like "objects are just magic hash references" and "methods are just subroutines with $self as the first argument" and "classes are just packages". In short, Perl OO teaches you to pay attention to how everything works which is the EXACT OPPOSITE of how OO is supposed to work.
OO is about NOT caring about the details of how things work. The whole point of an object is its a THING you ASK to do work and you don't care how it does it. A good object is like a good janitor. You ask the janitor to clean the floor, and then you walk away. When you come back, the floor is cleaned. It doesn't matter if the janitor used a mop, a toothbrush, their tongue or tore up the whole floor and installed a new one. The floor is clean and that's all that matters.
Furthermore, about the only way of composing objects that Perl gives you out of the box is inheritance. Inheritance is what everyone learns first when learning OO and its dangerous and mind warping. OO is OBJECT oriented, not inheritance oriented. The important thing is the encapsulation of the object, not that you can share code. A newbie programmer with inheritance is like giving a gun to the baby. Multiple inheritance is like giving them a howitzer. Newbies immediately leap to inheritance and created great tangled hierarchies. They never learn about delegation or composition or roles or mixins or any of the half dozen much better ways of letting objects share and build behaviors.
Moose gives you all that, out of the box, so you can focus on writing objects and not on writing an OO system.
Once you've learned how to do OO right then you can learn Perl's OO and how to do it twenty other ways, twelve of them wrong.