A .22 round will go that far (at least out of a rifle), but no handgun has the accuracy to do that. It's not a question of skill, even if it's completley immobilised in a mechanical rest and you've got a ballistic computer handy, it simply does not have the intrinsic accuracy to make that shot. Handguns are handguns and rifles are rifles.
Although even with a rifle that's a hell of a shot - all false modesty aside, in the military I'm considered an above average marksman. Using an open-sighted rifle (specifically a C7 or SA80A2) I can knock down a man sized target at 300 meters all day long, anything much further is pushing it. Combat-type scope (3.4X C79A1 or 4X SUSAT) helps, but not by that much.
As for the .45ACP round, assuming you're talking about a solid tungsten round (an FMJ bulley is, by definition, not a single piece of solid metal), it's not going to penetrate body armor with a trauma plate - that's a low velocity round with a low ballsitic coefficient. It's doesn't do range or penetration well. At normal handgun range it'll penetrate the bodywork on a car, most interior walls, but nothing really solid. A standard 230-grain .45ACP FMJ round will barely dent 3/4" aluminum (in fact, of all the varied handguns I've tried, only a 7.62mm Tokarev comes close to penetrating - very close, in fact), and I very much doubt that a steel or tungsten cored round would do much better. Small and fast rounds penetrate, big slow ones don't.
A Neilson device (just a muzzle booster, really) applies to recoil-operated locked breech firearms only, which these days are pretty much only (most) pistols of 9mm Luger calibre and above. A smaller pistol is usually straight blowback with a fixed barrel, which aren't effected by the additional weight of a supressor anyways.
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