First, well done on getting through your first dungeon!
Because of player scaling, DPS as measured on an addon meter is … weird. Whet a Level 32 sees is different from what a Level 11 sees is different from what a level 43 sees. This makes it very unreliable as a guide while levelling.
Icy-veins.com is indeed the website I’d send you to to learn your class at this stage as well, and spcifically their Easy Mode page for Ret: https://www.icy-veins.com/wow/retribution-paladin-pve-dps-easy-mode
Apparently, you don’t get your big cooldown Avenging Wrath (aka “Wings”) until level 48. I would have thought it was sooner. https://www.wowhead.com/spell=327979/avenging-wrath This ability is key to a Paladin’s burst.
Your gear is not terrible. Your Shoulders and Chest are weak, but it’s normal to have a couple of pieces lagging behind as you level. Don’t worry about it.
My guess is that, if your DPS is actually low (and I’m not sure of that) the cause is you hesitating instead of smashing those keys and going all out. That is the usual thing for beginners in dungeons who are a bit overwhelmed and distracted with all that’s going on. That goes away as you get more experience. Also, as you practice your rotation, it becomes muscle memory and automatic.
You can visit a Paladin Trainer and ask to be sent to the Proving Grounds for a bit of practice. Below max level, PG only allows you the easiest version, but if you are interested in performance, it’s worth doing.
You’re just on the learning curve. Keep going, but don’t take anything too seriously until you hit level 60, which is when performance starts to matter.