That's a good point about the flap.
In that case I think you'd probably do best to run it intermittently.
At 42W that's far less power required. Add the 10% factor and you're still only talking 46-47 Watts. Likely it needs a bit more to start up (the 108W it's rated at, I'd guess) but that's only a momentary spike until it gets up to speed.
Let's say you decided to run it at 5 minutes per hour. 42W x (5/60) x 24 hours = 84 Watt-hours. Now you can easily get that kind of production with a 20-Watt panel that gets 5 hours' sun as a daily average. If you had less than that where you're going to place the panel, a 30-Watt would be appropriate.
Since you're operating this thing rain or shine you'll need to oversize the battery a bit. That gives you leeway if you have 3 or 4 days without sun to replenish the energy you've used. Remember you don't often want to drain the battery past 30-40% or you'll shorten its life. 84 Watt-hours x 3 days would be 252 Watt-hours, and doubling that would be about 500 Watt-hours. That would allow you to go 3 days without sun and only drain the battery to 50% at that point. A 500 Watt-hour battery translates to about a 40 or 42 amp-hour (ah) battery.
Mrsolar has MK/Deka brand solar-appropriate batteries (good stuff) and they have a 32.5ah for $77 and a 55ah for $142. You might be able to find something else closer to you (batteries cost a lot to ship due to weight) but I'd caution against getting the cheap Chinese imports, from personal experience, I say pay the little bit extra for quality US-made brands. They're ok for experimentation but not so good if you want something that'll hold up over time. And don't get anything if it isn't made for solar applications. You'll want to build some sort of enclosure for the battery so kitty (or wifey) doesn't touch the terminals accidentally, and you may want to keep it next to a heated wall since batteries' performance will degrade if kept in hot or cold conditions.
Last major piece of that system would be a charge controller. Its main function would be to keep the battery from getting overcharged (in which case it can explode) but it also will give you a place to connect all your wires. I've had good experiences with the Morningstar SunSaver line. Pay the extra $10 and get the low-voltage disconnect (LVD) feature if you get one of these. Since at most you're using 1 amp for the fan, you can go with their smallest, the 6-amp model.
http://www.mrsolar.com/page/MSOS/PROD/m ... d429ce3728Then you just need an inverter capable of handling 150 Watts, which shouldn't cost you more than maybe $25 at most.
