How do I get an extra pet slot?

If you have a regular account then you can have 5 pets, if you have a Gold Account then you can have 10. If you want additional slots then you can either use the Mystical Donadak Plushie, which gives two extra slots, or the Mystical Montre Plushie which gives one. These can be bought in the Cash Shop, but you'll need a Gold Account to use the extra slots.