As you already know ICU experience is a must, at least a year and a lot of programs require 2. Get CCRN certified before you apply to schools. The advice I give everyone who ask me about going to CRNA school it this: Hundred and hundred of people apply every year, you need to stand out. If you haven't even started working in ICU yet you have at least a year before you can even consider applying to CRNA school. If you are really serious use this time to be a stand out applicant. Take graduate classes! Yes, there is a lot of work involved with taking graduate classes but it shows you are serious and you can handle graduate level work. Statistics, pathophysiology, anatomy, and physiology are all great classes to take prior to applying to CRNA school. You don't have to be a full time student, just take 1 class a semester. It'll pay off.
Also, research CRNA schools. Attend information session. Find the one that is the best fit for you. Study for and take the GRE, if you don't do great, take it again. So many new graduates get frustrated because they just want to apply to graduate school and get done. If your hospital offers classes, take them. For example, I took a course in reading 12-lead EKGs. Shadow a CRNA, most of them are more than happy to let you come in. If you in fact like it, then come back and shadow again. Create a relationship with that CRNA, they will make an invaluable recommendation. There is not a "fast path" but, as you can see, there are a ton of things for you to do while you are getting experience in the ICU. It is good that you want to start planning now, realistically you need a year or two for planning and preparation. Also, remember that you can't work while in CRNA school, start a savings account now so you don't have the stress of finances while you are in school. Good luck and remember to stay motivated, Rome wasn't built in a day, ya know!