Yes, there are 3 ways to activate a level cap:
Just rightclick your pet with the item you want them to wear while sneaking.
To remove the equipment just rightclick your pet with shears while sneaking.
Weapons/Armor are only visually and have no effect on the pet
Riding a pet is like riding a horse with a saddle.
Firstly look what you pet wants as food here.
Then just rightclick your pet while holding the food item in your hand.
It will first increase the saturation of your pet your pet and when it is at 100 saturation it will heal it. Every food item has a saturation of 6points and every missing saturation and HP will use 1point.