The rat is bugged. There are several threads about that. The problem was thought to be fixed, but the rat keeps escaping
When you play a bit longer, and hear the stories of how others start of the game was, you will know how lucky you are that you started when there was a tutorial to get you used to talking to NPCs, let you practice running without dying because you went down stairs, in an area where you do not fall through the floor, get money and tools, a warning about the death realm, and a role playing lesson as well, so other players will not ignore you later on for being disruptive

All you had to do was hunt a rat for two hours?

Many players will be jealous

OK, so you could have been even luckier and start playing a week later, when the bugs with tutorial are fixed
Anyway, all problems are solved now by the server just not working
