I agree with others; you haven't said what the wall's purpose is or
what the conditions are on the site.
If this is a retaining wall, it is low enough to not be too hard to do
if you get enough footing under it. I also agree yours sounds
undersized and your wall thickness sounds like too much.
If it's a retaining wall, what type of soil will it hold? Is it
expansive, like clay, when it's wet?
Is there any chance that you will have water build up (pressure) behind
it? If so, have you planned for drainage?
How much dirt is behind the wall in the sense of slope? Is there a
steep slope rising behind it, or is it level ground?
Will there be any unusual loads placed above the wall, such as a road
or driveway or a nearby swimming pool above it?
Does your climate present a frost heavy issue?
In our area, walls that are 4' or less don't require an engineer, but
that doesn't mean they aren't a good investment especially if you don't
know too much yourself. We don't have deep frosts, so engineering for
that isn't an issue. You can google retaining wall and retaining wall
drainage and learn a lot really quick.
Now, if this is just a decorative wall for a screen of some sort,
everything changes except for my $.02 your footing and wall thicknesses
still seem out of whack.