There was this one bit, during my first playthrough as a two-handed warrior, where I accidentally wound up on Vinsomer's island on the Storm Coast, and decided to try my luck anyway. Vinsomer was Level 19, I was level 16 (and most of my party was Level 15 or thereabouts; Cass might've been 16, but I don't remember).
Needless to say, this was the hardest dragon fight of the entire game for me, but it was also hands-down the most rewarding and exhilerating. Because it could basically two-shot everyone but Cass (whose AI cleverness and survivability as the Resident Tank has yet to be equaled by any other companion, even Blackwall with full Champion), I needed to rely far more on reading patterns and using Block and Strike (or whatever it's called; the Two-Handed counterattack that can be upgraded to build guard). Varric and Solas died so often, I almost ran out of health potions before I decided to save the last two for Trevelyan and Cass. So it was just us, frantically hacking and slashing away while trying not to get wiped by a single kick or spew of lightening, and it only got worse the longer it went on and the closer we got to killing it, because we would loose even more time and progress if we wiped further in. But, somehow, we managed to kill it. It was probably the most momentous, exhilerating experience of the game for me, and all other dragons seemed like child's play by comparison. Especially because, after the Vinsomer, I knew exactly what to do as a Two-Hander to safely beat them with minimal risk to myself. And that was before I even GOT the Reaver specialization, at which point the game became a self-destructive-Clawed-Fist-of-Vengeful-Holy-Fury-of-Pwnage affair, and nothing was ever fair for any enemy, ever again.
I also stayed up to three in the morning killing Vinsomer in this case. I'd meant to go to sleep over half an hour earlier, but as the fight went far better than I expected it to at the outset, and transformed into an incredible tale of triumph as it went on, I couldn't walk away.
So, yeah. Maybe try and tackle something the game says you're not ready for once in a while. You can sometimes beat it, and come out far better/wiser for it in the end.