Let's distinguish two forms of regulation, reflecting the statist vs. Hayekian distinction. One option is to make the undesirable activity illegal. The alternative is to make it costly. More generally, we can regulate activities either by using the blunt instrument of the law, or else by the more subtle manipulation of market forces. I think the latter will often be preferable.
Let's suppose that $1000 is more than enough to counterbalance the public health costs of a non-vaccinated person. In that case, what possible reason could we have for denying people the right to opt out of getting vaccinated if they care so much that they're willing to pay this cost?