Yes you can dig out the center of an 18' agp.
Keep in mind you should have an expandable overlap liner which provides additional liner material just for this. You won't need an expandable liner if your only going down 6" or so, but over a foot and you should upgrade to be safe.
I like to keep a couple foot flat area next to the walls all the way around, then slope the hole evenly from that point to the center being the deepest point.
Use a long piece of re-rod, use a tape measure and a string to mark the ground all the way around for the location of the actual walls (9'), and the start of the slope for deep center (maybe 6.5 - 7') Then ask the wife if she agrees with having that small of a shallow area around the pool for the young ones, and adjust to her thoughts.
I like to dig out the center to the depth desired (no more than 1.5' for 18' pool IMO - keep in mind the deeper you go, the more possibility you will have wrinkles in the liner, go a foot down and you will have a better laying liner) and use it as a goal to shape the bowl with a good flat shovel. You can use a spade for chunking out shovel fulls, but use a flat for shaping. Getting everything to be level and balanced is a little tedious, but take your time, use the center stake to verify and make a small 1' flat circle as the deep spot. Then imagine yourself standing in the deep spot with the pool complete, life is good.
Hope that helped in the plan, now you need some help actually digging the darn thing. Your going to be amazed at how dirt expands once you introduce air.
Oh, and welcome my northern friend. Stanley has been making the rounds here lately - Go Wings.