Hello! I just started and I'm level 20, but I'm struggling when fighting quest enemies. I feel like my skills don't do more damage than my regular attacks, and my dagger (I'm a ranger) seems to do more too. Is that normal? Is there something I'm missing?

No. Keep leveling up and upgrading your gear.

At level 20 you should grind at swamp until you're 24 and then move on to harpies. You should continue the MSQ after a bit of grinding. You'll gradually get there. Upgrding your gear should be top priority since this may be your first character. Later on, you will have gear ready for your future season characters. ;)

There are two things that affect how hard your skills hit, your AP and the damage multiplier of the skill.

If you are upgrading your weapons as you get beginner black stones (I'm assuming you are using the quest gear you are getting), it will get more powerful as you move along.  If you are on a season character you will also get Tuvala gear. If not, you can trade your Naru for Narchillan once it's PEN, which should happen around the time you finish the Mediah quest line at the latest.

When you get to level 37, unlock Descending Current. It's very handy.