Firstly, welcome to Eorzea!

Okay having a look at your Lodestone profile I can see immediately what your problems are. For a start, you have not yet upgraded your class (Marauder) to it's Job (Warrior). At level 30 the starting classes get 'Job' upgrades that increase their power and unlock new abilities that you cannot get otherwise. This is made worse by the fact that your class no longer gains new abilities by default after level 50, from then it's only Job abilities you get. So gaining your class's Job is pretty much vital and mandatory. But it's okay, you're still new so it's all a learning experience for you! (it doesn't help the game does not do a very good job telling you these things). And you did the right thing asking for help here!

Again looking at your character screen it says you do have WAR unlocked, but you just don't have it equipped, thus that means you've done at least the Job quest for WAR and all your class quests, so that's good. When you did the Job quest you would have gained a 'Soul Crystal' item, this is a special piece of equipment that you equip into the bottom right slot of your Character screen, and this will then automatically change your class to WAR. It's not permenant though, as it's dependent on having the crystal equipped. So open the Character screen in the main menu and click on the empty gear slot at the bottom right of the screen which says 'Soul Crystal'. You should have severeal there based on your Lodestone profile, but the one important for you is the 'Soul of the Warrior'. Click on it and drag it across to the slot, and you'll immediately change to WAR, which should raise your HP and stats as well as change your class's logo and name, but the level will be still the same (the Job piggybacks on the class so you're not specifically a Warrior, but a Marauder/Warrior).

Now that you have your Job upgrade, keep doing the quests the roegadyn WAR gives you, as these will give you some unique abilities you cannot get otherwise. Additionally, some of the later quests will also reward you with your Job's 'Artifact Armour' (or 'AF') - this is specific for that Job and is more powerful than the normal gear you can buy from a shop. I'm not certain but AF should have been enough to meet the item level requirement for the Thornmarch battle which you are now up to in the main storyline, failing that there should be level 54 gear available for sale on the Market Board that would even be better. This should be more than enough to at least meet the requirements to face down Good King Moggle Mog.

If you need any further help, please ask as this is what this section is for!