Thanks for your question.
No they do not. Animals when they die "perish" - go to oblivion. See Psalm 49:20. People do not go to heaven either, if that is any consolation. Apart from Christ, as the Psalmist says, people perish forever just like animals. The only hope for life after death for those "in Christ" is the resurrection at his return.
Here is some information from the website on this topic:
I hope you have found this helpful.