I wouldn't fight Rathian until you get better equipment, you probably wouldn't have enough time to defeat her within the quest limit. Assuming you don't get smacked by fireballs, poisoned by the tail, or eaten, that is. Though I haven't fought Rathian in single player, where she is apparently easier.
As long as you know how to avoid getting hit, Rathian's actually quite easy.
That's true of all monsters, not getting hit is the skill/strategy of this game. That's why monster attacks cause so much damage, so you can't just rush in and mash A and absorb every hit. Rathian is easier with a shield, since she has some quick attacks that can be difficult to roll away from. Also, all monsters are easier offline than online. Offline, they have less health and are less aggressive.
In single player, monsters always focus on me, so I can see what's coming. Online, monsters switch focus every few attacks, and usually I get hit by attacks meant for someone else. This is because if an attack isn't coming directly at me, the shield can't block it.