Hi Megan, welcome.
I have found the Australia - electrically certified hardware thread to be quite active and full of good local advice.
Would you be able to run an ethernet cable to where you want the camera ? If so, have a look at POE (Power Over Ethernet) since you get the benefit of fast secure communication and remove the need for batteries.
But generally I wonder if a camera would be the best option, since its view can be obscured (by say a car in the driveway), and it will detect other motion (like a courier delivery or a neighbours dog).
I assume you have considered adding a tag to the dogs collar, which could if you want to go all out, report its GPS coordinates to help you go find it ?