Pretty much what the title says, I'm just starting my first quest, I already have an in depth description of my character, but I was wondering if I could use that area to journal my progress? Or if there is a limit to how big it can get?

The character description page is fairly generous, but it is not limitless.  It's probably the same as the limit on the size of a single post -- 51,200 characters or around 10,000 words.

I don't know that there's a limit on the description...but since it's what everyone else sees about your character when they look at the cast list, I wouldn't consider it the best option for keeping a 'character journal' (unless it's in the form of various 'worn trophies' from defeated opponents...)

Many, if not most games have character sheets available, which, to my knowledge, aren't limited in size, and only you and the GM can see the character sheet.  Or, you have a scratchpad in each game, that's got...is it a 10,000-character limit? I don't know, I don't use mine much, although I've found it useful to make note of significant NPCs that I've interacted with in the past, so I can reference them again.  You'd have to be concise about it, using that for a journal...but it could be done.

But I would recommend either of those for a 'journal', rather than your description.  If the character sheets aren't active in your game, you could ask your GM to make them active, and explain what you want to use it for.  But I think stuff like that was part of the original intent behind the scratchpad feature...

Another option might be to ask the GM to create a thread specifically for you to use as a journal...depends on how heavily the GM relies on different groups in the party and how many players are in the game, but he could create a thread, set its access to Group K, add you to that group...you and he are the only ones who know its there, and you've got a lot of space for a journal...

Some GMs I have played with set up a journal thread where all players/characters can keep track of events and such.