Abso-friggin-lutely you should apply!
Faking it till you make it is as American as apple pie! :)
All joking aside and in my humble opinion when you're job hunting you should always aim for a higher position and more money. It has been my experience that that new title and responsibilities seems a little scary at first but once people get to know you and trust you a bit the situation seems to relax and you get used to it.
I once took a teaching job at a vocational college teaching a subject that I knew nothing about. To get the job I had to teach a lesson to my supervisor, fellow instructors, campus director etc. I spent two days learning all I could and planning my presentation. It went over well and I got the job and I have since become certified in the field of study and have taught off and on for about about 8 years.
What I have learned most about being in business and as a CFO I understand the accounting profession you are working in a bit, is that your technical skills are not nearly as important as your communication skills and just being a responsible, patient, honest human being who shows up willing to learn and work hard. If you are lacking the skills or experience you can get them as you go. In accounting you can always look to see how it was done before or just google it if you are unsure. I also highly recommend learning as much as you can about the overall business you are in not just the specific aspects of your day to day job.
It never ceases to amaze me how some intelligent people who have plenty of technical skills are generally disliked and then negatively branded because quite honestly they are jerks with poor communication skills and no patience.
Best advice I can give you? Never put a title on a pedestal. Once you achieve it you realize it's not that awe inspiring. So don't stress the technical skills as long as you are not a jerk and are willing to learn you can handle it.
As Nicholas Cage said the "The Family Man"
"Business is business. Wall Street, Main Street; It’s all a bunch of people getting up in the morning, trying to figure out how they’re going to send their kids to college. It’s just people, and I know people.”
Good luck.