Welcome to the server!
The best way to find guilds is to search in-game (Stormwind, Stromgarde and Duskwood are the most popular Alliance RP hubs), browse server forums, check Argent Archives
https://www.argentarchives.org
I´d however suggest to rethink the plans for the concept, specifically the black dragon part. If I understand it correctly, the idea is to start as somewhat low power concept, a dwarf who joins a group of ordinary soldiers, and then after some time leaves it to do some stuff with black dragons. This is going to be a big red flag for any guild officer because you´re basically saying that the guild is going to be a stepping stone for your own stories, effectively being NPCs in your character´s journey.
In DnD terms, imagine if you came to a group running their own game, said “I´ll be here with you for few months, then I´ll leave because I´m not that interested in the campaign you´re doing”, and expected to be accepted by them.
Secondly, and this is a problem I´ve seen done (and did myself before) by many players: I´d suggest against making some huge plans for what is going to happen to your character. RP is a collaborative effort and you don´t know where things will lead you. Also, sometimes following up on that plan will lead into a situation where you won´t be able to find RP because there won´t be anyone RPing concepts that will vibe with yours (and dwarf riding a black dragon is going to be one of those concepts that will find it really hard to find RP).
IMO the best way to start would be to create a character without any big plans for what you want to do. The concept of Dark Iron dwarf who lost his friend is fine (although keep in mind that Alliance and Horde have been at peace for 5-6 years now, with the exception of some small skirmishes that only got off-hand mentions, and Dark Irons have been hostile to the Alliance until 12-13 years ago), and would be accepted by many guilds, whether they´re military guilds, adventurer/mercenary guilds, or ones with focus on dwarves (I think Dwarves of Morodnir are the only one now, but there might be others that don´t advertise on the forums). Just make sure to keep it simple and see where the RP takes you.