That's not the issue with HIV. The issue with HIV is that it's a retrovirus. It uses both reverse transcription and inscription enzymes to change your DNA.

A vaccine works to stimulate your immune system's "memory" that's evolved for treating infections. (That can be anti-bodies, but it's more complex .. also involves memory T-cells, the complement system, etc.)

When the same virus comes it, it will infect cells, but your body is much more prepared to handle it. The trouble with HIV is that it's the initial infection that can slowly inactivate an immune system over 2~5 years (not everyone though. Some people have HIV and never develop AIDS; known as Long Term Non-Progressives).

A vaccine wouldn't help at all with HIV. Keep in mind, the HIV rapid test checks for the presence of antibodies.