I don't really consider it copying.
I don't consider the Littlest Pet Shop digital pet a virtual pet. You don't have to care for it- you can leave it for months or even years and it cannot depart/pass away.
In the Tamagotchi you can have several little goals. On the older versions you could try and get a certain character or see what is the best character that you can get. On all the versions with a Gotchi Point system you could try and get the maximum amount of Gotchi Points or try and get a certain item like the UFO. On the Familitchi or Famitama, you can aim for 100% bonding percentage as well as trying to get a special family. On the versions with jobs you can aim to get a certain job, or to earn enough skill points to get a secret character. On the v3, v4 and v4.5 you could try and collect all of the souvenirs. On the Famitama or Familitchi, since there is enough room to buy every item without having to delete any, you could try and collect all of the items! You see, there are a lot of goals you could set for yourself.
On the Littlest Pet Shop however, there only really is one goal and that is to collect all of the stamps. Once you've done that, there isn't much more that you can do! Sure, you can feed and groom your pet but that doesn't do too much plus there's no big penalty for not doing so. There are little penalties however- if you don't feed your pet it walks really slowly until you feed it again and if you don't groom or play with your pet it may refuse to do stuff until you groom it and give it a toy. I have a dog Littlest Pet Shop. It may be cute but I've completely lost interest now. I almost forgot I still have it!