Hi Kemya, welcome to the community!
You’ll find there are some guilds that exclusively focus on raiding, even on Argent Dawn. Some raiding guilds also do some casual RP on the side, though with those you generally won’t see the same level of depth and commitment as a pure RP guild.
Lupús’ idea would work - alternatively you could have a few RP characters and a few raiding characters, all on Argent Dawn.
I believe there are also a few communities for those who want to run non-PUG raids without leaving their RP guild; it’s organised on Discord, by my knowledge.
That’d enable you to do both on the same character.
The stickied raiding progress forum thread has been discontinued by the looks of it, so to find a raiding guild, you could have a more extended browse of these forums. And Frigel’s wowprogress link there should point you in the right direction.
You’re bound to find a few raiding guilds to choose among, I see such guild threads pop up at least once a week. You could also look for one in-game through the general or trade chat channels.
As a word of warning – You’ll find that raiding guilds and raiders in general tend to get a bit of a lukewarm welcome from RPers.
This is because of a fear of ‘lolling’, which is a type of trolling or harassment where people actively sabotage RP by spamming nonsense, jumping around, placing toys and mounts in RPers’ way, and so forth.
As long as you don’t deliberately disrupt others that way (and avoid associating with those who do) you should be just fine. 
Again, welcome to the community and I hope you end up transferring! If you’re unsure where to start I’d warmly recommend having a read through this excellent starters’ guide by Spradley.