+ solar panel controller to control the charging of the car battery, Jaycar has then for $35. There are more than enough 12v pumps around, no need to add inefficiencies and cost of an inverter.
A car battery will be destroyed pretty quickly if you draw more than about 5 amp hours or 60 watt hours from it before recharging. They really suck for anything but high instantaneous loads, even the 5 amp hours will slightly damage it. You'd probably want to limit yourself to a pump that won't draw more than that over about 20 hours. So that leaves you about 3 watts maximum draw.
You'll need a solar panel that will top that off each day even in bad weather, so on top of the 3 watts you'll want a solar panel that will top the battery off even mid winter when you'll get some 8 hours of daylight, but it will be cloudy frequently so probably need something that can produce that 60 watt hours in full sunlight in 2 hours. If you don't you'll never even top off the battery on a dark day damaging it So, at a minimum you'll want a 30 watt solar panel. Your options from Jaycar are a 20 watt for $180 that isn't really good enough so you'll want a pair or a 40 watt for $455.
So we have, a car battery $100ish, Solar panel for $360ish, controller for $35 and then you have the pump. This is all before buy the pump.
First place I'd improve though is the battery, like I said, lead acids SUCK for this kind of thing. If you build a 10 series nimh pack though, you can get buy the batteries off Trademe for about $120 and they don't mind being discharged more than a tiny percent. So they'll probably last a LOT longer.