Charging more for a product to allocate demand doesn't necessarily increase profits. If the profits aren't invested to raise production at the remaining farms, e.g. if supply is inelastic, which it might be in the short run (raising new chickens at farms that got bird flu would take just as long as at healthy farms, you can't force existing chickens to lay more eggs, etc.), then the profits ought to be rebated back.
In fact, retaining profit can be a sign of price gouging. It means you've run into inelastic supply and there's no place to spend that money to solve a short-run problem. On the other hand, maybe they'll reinvest it next year or over the long term into expansion, and you might want to reward investors and management at well run farms; but if this flu is a freak accident of nature where equally run farms might get it or not, then no.