Dps is usually affected by 3 things.

1. Rotation/Light attack weaving is the most important. Getting the timing of this down is the key to high dps.

2. Cp does matter towards higher dps, so numbers will improve as you increase your cp. Baby characters aren't really going to pull great dps, because they don't have full access to skills/passives,etc. Only having 300+ cp means you're going to be losing out on penetration/crit damage, etc. I would focus on leveling cp higher, especially right now with the double xp event going on.

3.Third would be gear. Try to make sure your character has the right type of gear for what you're trying to do.

get lvl 50 1st to get proper gear on max lvl
if you are under 50lvl you shouldn't care to much about your dps as you dont even have option to enter on veteran content where mostply people can whine at your low dps

for starter crafted julianos is good enough for dps and mother sorrow to buy as 2nd set or medusa which is to farm from arx corinum dung, after this you can go farm sunspire trial for false god set instead julianos to have sustain to keep dps

rest will lay on your skill and skills, rotation you will be using which also you wont have full til most probably max lvl of character because you wont unlock so fast all skills, passives need in your dps build

8k Dps singletarget in low lvl with 300ish cp seems okay. I hit around the same on my second account with 200 cp

I made a video awhile back where I showed my rotation on a 3mill. I was CP261 asking for help.

I could reach 15k but wasn't able to sustain it.

Light attacks were off.. (Only went through every other skill)
Armor picks were off

And honestly...

CP helps doing a F-ton of damage.
The damage potential of a cp 300 and a cp 810 is night and day.

As people have already said I would advice you to get a target dummy.

I think the 3 million target dummy is more beginner friendly, personly.
Put on some parse food (Max ressources + recovery)

Find a rotation and sloooooooooooow it down.

Skill... Light attack... skill... light attack...

As you get more familiar with rotation you can shorten the gab between hitting your light attacks and doing the skill. Make it more fluent.

After you got a rotation you start using it in dungeons to get familiar with it - while you farm for gear. So once you got your gear you'll be battle ready.

This is were you gold out your gear - especially your weapons.
You transmute you get the proper traits.

For CP360 aim for hitting 20k on the dummy

Once you've shown yourself you can hit that number try to keep 20k going and sustain it.

Once you're able to kill the 3 million dummy with a 20k parse you'll be able to roll through base game vet, and probably be better than 70% of your fellow DDs in PUGS.