With any class that grants you a familiar you can have a respectable cat dancer starting at level 1. The familiar has the same ranks in skills that you do. If you take a rank in Perform (dance) your familiar will also have a rank in Perform (Dance).
Skills: For each skill in which either the master or the familiar has ranks, use either the normal skill ranks for an animal of that type or the master's skill ranks, whichever is better. In either case, the familiar uses its own ability modifiers. Regardless of a familiar's total skill modifiers, some skills may remain beyond the familiar's ability to use. Familiars treat Acrobatics, Climb, Fly, Perception, Stealth, and Swim as class skills.
It is important that the cat has a rank in Peform (dance), because the Entertain trick requires ranks in Perform in order to use a Perform check instead of a Charisma check and we are going to be adding bonuses to Perform.
Entertain (DC 25): The animal can dance, sing, or perform some other impressive and enjoyable trick to entertain those around it. At the command of its owner, the animal can make a Perform check (or a Charisma check if it has no ranks in Perform) to show off its talent. Willing onlookers or those who fail an opposed Sense Motive check take a –2 penalty on Perception checks to notice anything but the animal entertaining them. Tricksters and con artists often teach their animals to perform this trick while they pickpocket viewers or sneak about unnoticed.
The mascot familiar archetype makes Perform a class skill.
Class Skills: A mascot treats all Perform skills as class skills.
The evolved familiar feat will give your familiar a single 1-point eidolon evolution. The skilled evolution gives a +8 racial bonus to any one skill.
An eidolon becomes especially adept at a specific skill, gaining a +8 racial bonus on that skill. This evolution can be selected more than once. Its effects do not stack. Each time an eidolon selects this evolution, it applies to a different skill.
This gives your cat a +10 Peform (Dance) check (1 rank, +3 class skill, -2 Cha, +8 racial bonus).
The master needs to have 13 Int, 13 Cha, the familiar class feature, the evolved familiar feat, and ranks in perform. The master will also need to be able to make a DC 25 handle animal check to teach the familiar the Entertain trick.