How can I know if I am able to pursue a PhD? I am a 3rd-year computer engineering student at a mid-tier state school with a high GPA (3.97/4.0), top of my class, and 1 semester worth of research. I am also currently participating in a very prestigious REU program, so I do have a decent amount of research experience. I have also taken the GRE and done pretty well (mid 80s) percentile in verb/quant and 99th percentile in AWA. I've also basically narrowed down my research interests to 2 fields, so I have a general idea of what I'd like to specialize in. My goal is to become a Professor in Electrical and Computer Engineering, and I'm starting to contemplate applying to grad schools. I really want a PhD because I know that it is absolutely necessary for my goals. 

My only problem is that I am afraid of doing the PhD, because I feel that I won't remember everything (or a good amount) of everything from undergrad. This especially scares me because despite my successes in undergrad, I'm not sure that I could pass the qualifying exams. I guess I'm just afraid of the unknown; do you think that I should just go for it?

Thanks, sorry if my question comes off as rambling; I really want to earn a PhD so I can be a professor or faculty member at some point and knowing that I could fail is very scary.
Talk to your professors. They've been through PhDs themselves, and they know your capabilities much better than anyone else to boot.

Having said that, if you have both a very high GPA and research experience (which you did not dislike), you should be more than qualified to do PhD studies. If you aren't qualified then nobody else in your cohort is qualified, which is not believable. Besides, if you want to become a professor, you'll need to get a PhD - since it's something you must do, you might as well attempt it (or change career goals).