The Gardening and Landscaping site had a very similar request, regarding climate/location details which are useful to know when answering a question. I much agree with the following statement on such:
If [the data] is important to the question, that information should be included in the text of the question itself — or edited into the question, if it is missing. Displaying that information automatically for "times when we forget" could actually cause users to exclude that information from the question explicitly.
This rather links with Larry's answer, the information may not be fully static or apparent for a single user. Furthermore, you could end up with a different vehicle later on in life, not just with more cars, and so the information from your card may not reflect the vehicle which the original question was asked about.
Ultimately, the important point is that if hte make and model could or are relevant to the question, it really should be in the question body. That allows the question to exist independent of the author, which is a lot of how the sites operate - the questions are their own entities.
That said, there is an option, which conveniently also has a Landscaping mirror. With enough reputation to be an Established user (750 is the requirement, currently), you gain a "hover card" that shows whenever a user hovers the mouse over your avatar. You can use this to store information on your car model for easy lookup.
This alternative should not replace the need to include the information in the question body. Relevant data should always be found as a part of the question, not needing one to look up the author directly.
It will, however, make it easier in the chance that you do forget, and will allow other users to easily find that information and edit it in should they beat you to the punch. However, please don't use it as an excuse to continually forget that information. ♪