The ripple effects through the economy are probably the longer term worry. Daily prices are certainly going up but quoting some futures price and multiplying by estimated gallons used doesn't work for airlines. They are in long term contracts at rates far lower than spot. Fare adjustments and fuel surcharges will also help.
Smaller carriers, especially if already in financial distress, are a worry. We're all (especially those who started 2000 or prior) hardwired to see black swans everywhere because we've been burned more than once. This might be one and it might not.
As always keep your furlough/downgrade fund topped off. Keep your FO house, etc.