There are a lot of moving parts, so it's really hard for me to estimate the cost here. It's done somewhat routinely in some institutions (although it is very, very expensive).

You first need to make humanize mice (i.e. mice with human immune systems). Luckily we can make those by taking NOD/SCID mice (an [expensive] immunodeficient mouse line) and then colonize them with human hematopoietic stem cells from a human donor to reconstitue the immune system. Then you have to do a lot of experiments to make sure your humanized mice can mount immune responses. Then, you can test your peptide and see if your humanized mice will make CD8 T cells to your peptide... Finally, you can infect your mice with HIV (now that you have a humanized immune system) and see how your vaccinated vs. unvaccinated mice fare.

I have no idea what the downsides of this approach are because I don't work on HIV or with humanized mice--but mice ain't people. So after all that work you'd have shed limited light on what would happen in real people.

I would argue that a better approach is to see whether HIV patients have actually made CD8 T cells against these antigens. This can be done more inexpensively and would give you pretty good evidence that your peptide is immunogenic in real people.