Cat hat can be found in New Ark. Take the stairs next to Hardware R Us and head all the way down.
There's no need to pick up the lipstick kit, unless you want to keep one for yourself. It's in Skin Deep all the way in the top left of Upper New Ark. If you're going to go that far, might as well also visit Poppin' Stop to see if they have the monkey and frog animal onesies.