I'm in a small town, too. Actually, I thought I recognized your similar small-town stories from a previous post, so checked your prior topics and saw I'd commented on one when you were looking for a job before. 🙂 But as I said there, I'm in a town of about 3,000 people; next towns over are 7,000 and 8,000. Specifically in the town I live in, there's not many people who move in or out of town, so everyone knows everyone and is related to most of them. My family moved to town a few years ago, then the rest of my family moved away, so I'm a stranger in town with an accent to prove it whether I want to or not. So, I understand the small-town thing, and also somewhat the small-town outsider (not sure if you're still feeling that way, but from your prior post it sounded like the small-town everyone-knows-everyone-but-I-don't was part of the issue). The area I live in has a poor economy and low wages. My first job was in public accounting and paid about half of what you're getting paid (was $8/hr, got a raise to $9/hr)…and this wasn't back in the dark ages – just about 3 1/2 years ago! So, I completely get where you're coming from.
That being said…
I would definitely agree with what others have said about ensuring that you have a new job opportunity lined up before doing anything that could jeopardize this one. I know how rare accounting job openings are in a small town, especially ones that aren't already filled by someone who knows someone who is related to someone, so to do anything that could mess up your job future where you are without having something else lined up wouldn't be a good move. Demanding a certain figure of a raise is an example of something that would, in my mind, jeopardize your current job. Do you know if your current employer bills out based on the credential of the person doing the work, so would bill out at a higher rate for work that you do as a CPA than work that you do as a non-CPA? If so, then they'll be making more money off of you, and I think a more substantial raise – in the $5-7k range like you're hoping for – is more likely. Not for certain, but that's the only way I'd see it happening. If not, then the only thing that makes you worth more today than you were on the day they hired you is the knowledge that you've gained since you started working for them, and they'll likely feel like they “earned” that knowledge to some extent. So, if they don't bill more for your work as a CPA than they did as a non-CPA, then I would anticipate a smaller raise – say 5-10% on a good day, which would be 1.5-3.5k.
Generally speaking, you're more likely to get the raises that you “deserve” by switching jobs than by getting raises. At my first job, I got a $1 raise (which, granted, was around 12.5% because my pay was so low to start with), and it was pretty clear that was all I was getting for a good while. So, I switched jobs after about a year, and got an approx. 50% raise. Now, given you're starting higher than I did, I'm not saying that you're guaranteed a 50% raise, too, but I think there's more potential for getting market pay by switching jobs than by sticking around for raises. (Note: a 50% raise was market for my credentials at the time and for my area…like I said, pay is low here. That was still less than $30k/yr, but it was good for the area.)
As to your question of whether a year is long enough or not – the only way to really know is to put some feelers out there and see if you get any “bites”. Start watching for jobs and applying. Be aware of how tight-knit the public accounting world is, though, if you're wanting to stay in public. I was jumping to private after my 1 year in public, so wasn't too worried about word getting back to my boss that I was looking; however, the public community where I worked was pretty tight-knit, so I would have been hesitant to apply to other public firms, since he knew most of the owners and I would have been concerned that they would have called him and said “Hey so your employee is applying here..”. So, be aware of what connections the owners of your firm have and what impact that may need to have on your job search. Still, though, the only way to know if a year's experience is enough to improve your job search is to try your job search and see if it goes better now than it did a year ago. For me, a year made a world of difference – it was enough to get me into private accounting, which is what I'd wanted to do but a field which always required experience.