I would do basically what you are thinking... get a wireless WiFi camera with IR on it (so you can see it at night) and then set up a 20-40W solar panel and a lead-acid battery charger and then deep-cycle marine battery, and then drive the WiFi camera from the lead acid battery. Ideally the WiFi camera would run on 12V DC, but otherwise you'd need a DC-DC converter or - less efficient - get a cheap car inverter and then go from 12V DC from the battery to 120V AC to whatever the camera wants. To boost the signal across the 1/2 mile, you need a clear line-of-site with no trees of any kind, 2.4GHz doesn't penetrate water at all in the air or in the leaves of the trees. 2.4GHz was specifically chosen for free WiFi wireless because it's such a useless frequency due to this limitation. I'm not sure what size solar panel you'll need - depends on what the camera needs... but you can do the math what you need to charge the battery and cover the camera during the day and then a battery big enough to get you through the night without draining past ~50% (if you drain too far each night, the battery won't last long).
And then you will want a better antenna. Something like a "cantenna", a 2.4GHz yagi, or a parabolic antenna. Something that has some sort of directionality. A yagi would be best. Something like this:
http://www.amazon.com/Browning-2-4-G.../dp/B003YL5WJG I don't believe the guys on Amazon quoting 25dB - so steer away from anything super cheap with high dB numbers because they don't seem realistic. You might need to put a yagi on both ends of the link - one in your house pointed at the coop and then another at the coop pointed at the house. I don't think you need to amplify it - just highly directional antennas and you should be set.... as long as there's no trees. If there are trees, you might need/want amplifiers. I'd start with a yagi on the coop first and then put one on the house if the link is too weak and then up to amplifiers if needed... but you'll need two amplifiers for each side and that will up your power budget on the battery+solar.
If you opt for this, make sure to oversize the battery substantially - you really don't want to be draining it substantially at night, and it won't work as well when it's cold, and on cloudy days it won't charge as much... so get a beefy battery because otherwise you'll be replacing it frequently (like every 4-6 months).