First off, make sure the back door has a couple of secure locks, at least one way taller than your child will be for quite a long time. That way if your child figures out how to open the regular one, the other one is not so easy.
Next, I would get a fence that is like the one surrounding your back yard. If it's a 6 foot fence, then go for the 4 foot version. That way it conforms to the decor. Make sure that there are a couple of locks on the fence gate as well. If the fence is chain linked, don't put chain link around the pool. We had a 3 year old in our area climb it and drown.
You might also try to explain to the child pool safety. Simply put, stove is hot, get burned, pool is bad, you can drown. I know they are young, but the know when Mommy is serious about something. So start the training now.
I agree, keeping the child in eye sight is the best, but having raised basically two sets of twins.......it's harder than it sounds. So just make sure that you have plenty of locks and plenty of safety gizmo's........you might even put an alarm on the pool gate to make a noise when someone goes in or out.....I'm sure they is some sort of movement detector that can be either put on the gate or inside for when the gate opens. Just make sure it's loud!
Good Luck and enjoy your new home and pool.