Black and white film is typically more forgiving of slight exposure errors than colour film - photographs that would look dull and lifeless in colour can look moody and dramatic in B&W. Having said that, however, it’s important to get as close to a good exposure as possible.
As friedo noted, the Sunny 16 rule is a good place to start. I wouldn’t shoot the picture at f/16, though, for two reasons. The most important one is that at F/16, you’d essentially have an infinite depth of field - the subject and the background would both be in sharp focus, making the background a distraction. You’d get a much more pleasing blurred background if you shoot at a larger aperture; say F/4 or thereabouts. This, for example, was taken at F/2.5, from a distance of about 2-3m.
I’m not sure how much you know about the relation between shutter speed, aperture and exposure, so forgive me if this is stuff you’re already aware of.
Having a larger aperture (smaller F number) means a wider diaphragm on the lens => more light coming in => higher shutter speed. I’m assuming you’re shooting with a standard 50mm F/1.8 lens (which is what most AE-1s came with, IIRC) which means your creative options are quite wide. Moving from F/16 to F/4 means going up four stops (F/16 to F/8 is two stops, and F/8 to F/4 is another two), so your shutter speed needs to be doubled 4 times. In other words, 1/6400 of a second at F/4 will give you the same exposure as 1/400 of a second at F/16, so you’re still following the Sunny 16 rule. Your camera can’t shoot over 1/1000 of a second, which is a very good reason to use slower film.
In shady conditions, I’d typically allow one stop less, so I’d be shooting at 1/200 at F/16, or 1/800 at F/4. I think you might be better served by shooting on a cloudy day, partly because there’s less light (which in this case is a good thing) but also because the light is softer and more diffuse. Portraits in direct sunlight can be very unforgiving, with harsh shadows and too much contrast. At the very least, you should look to using a reflector of sorts, if it’s at all possible, to balance out the light.
Shooting outdoors allows you plenty of latitude in terms of type of film, so I’d look to getting slightly slower film (ISO 200 or 100), also as noted by friedo. I wouldn’t say that you need a tripod at these shutter speeds, though, but it never hurts. As noted above, it will also allow you to use a larger aperture and get a more pleasing portrait.
Sorry if this is all a bit too much; but feel free to ask questions!