There is a "Fleet" module in Odoo Community Edition, if you can get that to work. You can setup a great deal of details there including stuff like maintenance dates etc.

You could also consider setting up several calendars, one for each car. Treat each car like a room or calendar and you could assign occupants for it - driver/passenger perhaps.

You might be able to use a Gantt chart for planning when vehicles might become available in one of the project management tools. Odoo has Gantt functionality too.

I found https://www.damoov.com/telematics-app/ and http://www.qwicksoft.com/open-source-code-taxi-cab-dispatch-management-software.html (http only!). Not sure if those are what you are looking for.