Rats are all over the planet, especially where humans are. While there are 2,200 species in total, the most well-known are beavers, guinea pigs, squirrels, and mice. Rodent-like creatures have been on Earth for around 66 million years, which means they appeared right after the extinction of the dinosaurs.
You are right Amos, everything was created in 7 days by a magic man in the sky.
Carbon dating is not relevant here since it only can date thing that are 50000 years or younger. There are other methods for older things. The theory of evolution makes sense and can explain a lot of the observations that have been done by scientists.