I have client that wants to know exactly how many hours/minutes a project has taken. Does AE have a timer or something that gives me a better gauge of time worked on a project, as opposed to just looking at timestamps on filenames..?
No. You could use a script [link] to track your time, or you could use a separate application, or even just a paper log -- but these must be done as you go, not after the fact. If you're a time-billing freelancer, accurately tracking your time is something you should be used to.
When I track time, the most granular I'll ever get is an hour. Asking about a project in terms of minutes seems a little intense.
You can get started with the free version, and see whether it fits your work style, then buy the full version for $49.99, or subscribe for $24.99 a year. I bought the full version. It allows me to track my time (I don't bill my clients from within the program, but you can), and I can create categories whithin my projects, so I can see exactly the amount of time which goes into pre-pro, production, post, etc.. It can be a real eye opener! ETT is a small company, so you can actually contact the programmer if you have questions or problems.