A free time tracking software I utilized when I first started was
HourGuard. It is installed on your local computer, so it is not available online. It worked pretty well and has some good reporting.
Other VA's like the time-tracking plugin with
FreshBooks, but I never liked this program.
Once you have a flow of income you may want to consider moving to a Project Management system that includes time tracking. My favorite it
myIntervals. For $20 a month you get a ton of features.
Best of Luck,
Julie