Should you get a new pet? And how soon? Only you can answer these questions. Some people cope with the loss better by adopting another pet right away, others need time. Some feel that by getting a new pet they are “betraying” the old one, and therefore refuse to do so.
I don’t think that getting a new pet shows disloyalty to the old one, or that you have easily forgotten and replaced them. Your memories will always stay with you. You did not stop loving your pet the moment they died, and who says you cannot love more than one?
Children can be very sensitive to it as well, they might resent the new pet for trying to take the place of the old one. “I don’t want this new dog, I want my Tommy!” is a common reaction. That is why it is very important to make the decision about taking a new pet together, and explain to the child that you are not “replacing” Tommy. You still love and remember Tommy, and you are getting a new friend to love. Tommy would not feel bad because of it.
It is usually not recommended to get an exact look-alike of your old pet and especially to give them the same name. Do not try to deceive yourself into believing that you have your old companion back, you know it is not possible. This new pet is different, it will behave differently and never live up to your expectations of being just like the old one. Accept your new friend as they are, and love them for it.
I have had many pets, and it does not get any easier when the time comes to part with them. But I think the joy they bring into my life is far greater.