After completing Gertrude's Cat, Gertrude gives you 1 kitten for free. If you lose your cat, you may buy another kitten from her for 100 coins. She won't sell you more kittens if you can start or have just started Ratcatchers, since she will only talk to you about the quest until you finish it.
With the activated ring of charos you can choose the colour of your new kitten. Doing this is required to complete the Varrock medium task, A Lick of Paint.