7805 will handle 1A at 12V input fine, so long as you use a big enough heatsink.
You'll need heatsinks anyway as 7W is too much for two bare TO220 packages. 1W per
package (without heatsink) is pushing it, use heatsink!
But you'll be better off using a cheap switch-mode DC-DC converter like the eBay LM2596 units,
much higher efficiency, no heatsink needed (only downside is the noise which could be an issue
with sensitive low-voltage analog signals).