I am not sure that you will find an attorney on here who will unreservedly tell you it is "OK."
On the one hand, you're simply using a doll to create an original character, in a video that you will be selling. People do things like this with dolls and puppets all the time. A band called Aqua even wrote a song and made a music video incorporating (and mocking) Barbie.
On the other hand, Mattel then sued Aqua. Eventually, Aqua established "fair use" of the Barbie image and trademark in a parodic sense; their song and video were an artistic comment on Barbie as a cultural signifier and influence. Thus, after spending many many thousands of dollars to defend their position, Aqua achieved a favorable ruling.
The use you're proposing is clearly not a parody. If anything, you may be leveraging Barbie's reputation of blond cluelessness to solidify your "original" character. Thus, even though you may not consciously intend to do so, you may be making Barbie's identity a central feature of your video.
Additionally, it is a bit silly to say that you are not "trying" to associate a Barbie doll to the entire franchise and brand identity. Barbie is iconic around the globe. There is no way that you can hold up a Barbie doll, and not immediately flood 99% of viewers with roughly the same set of ideas and expectations. Simply by including the doll in the video, you necessarily do imply the Barbie identity. This raises issues of false endorsement, false light, tarnishment, or dilution.
Mattel is known to be litigious. Presuming that Barbie's identity is *not* a central aspect of your video, it would be wise to consider using some different doll to represent your co-host.
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Attorney Harrison mentions a point that would be the most useful in your situation, the "fair use" defense. In addition to the parody part of "fair use," the "fair use" doctrine also looks favorably on use for educational purposes, which your course appears to be. I would highly recommend meeting with an attorney to analyze how you use the Barbie doll to see how strong your "fair use" defense would be. While no attorney will be able to tell you that Mattel won't sue you, they can give you an idea of how strong your defense is and that could affect how you would approach the situation if Mattel decides to threaten suit.
The above discussion only applies to possible copyright infringement. While I have not performed the research to tell what Mattel's trademark protection is in the doll, there could be trademark issues as well. If you are using the Barbie in a way that nothing leads the consumer to believe that Mattel either produced or endorsed your course you should be fine. When you take the video in for review of the copyright issues by an intellectual property attorney, I would ask him/her about the trademark issues as well as the attorney should be able to determine your trademark liability from the same review.
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My colleagues offered some good advice here and I think I agree with their remarks.
Given that you do not in any way require that this be a branded doll, that is, the fact that the doll is a "Barbie" is not relevant (at least as I understand it) to your purpose,. I strongly advise using a more generic doll so to avoid the rather hyper-sensitive Mattel policing regime.
My colleagues noted "fair use." Nothing you described here suggests that you would fall under a qualified exception. For example, a parody requires that you comment on the material (the Barbie in this case), its creator (Mattel), or the message or perceived message that the work is making. Merely using someone's product in a humorous scenario does not make it a parody. There is no general exception for educational purposes either. The exception, statutorily, exempts non-profit educational institutions for using copyrighted material in a classroom learning environment for non-commercial purposes. So if this was a public high school, for example, and part of a communications class exercise, no infringement claim would stick. But if, however, this was part of a skit being produced for a public performance at the school's theater the exemption would not apply. Remember too that fair use is a defense is not something that keeps you from being sued. It is how you would defend yourself should that happen.
I would consult a lawyer in private and discuss in more detail. While my colleague went out of his way to disclaim that he is not a lawyer in KY, I just want to make clear that you are in fact permitted to use a lawyer that is located wherever so long as that lawyer has a license to practice where that lawyer is. In this case it is even less relevant because US copyright law is federal and uniform. This is not to say that you might prefer to work with a local lawyer and you can use Avvo to help locate one by going to the find a lawyer tab up top.
Most of us here, including myself, offer a free phone consult.
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Find another inflatable doll and call it Barbie or whatever you like.
Do not mess with Mattel unless you have deep pockets.
USPTO Registered Patent Attorney, Master of Intellectual Property law, MBA I am neither your attorney, nor my answers or comments in AVVO.com create an attorney-client relationship with you. You may accept or disregard my free advice in AVVO.com at your own risk. I am a Patent Attorney, admitted to the USPTO and to the Florida Bar.