Coding style:

• Space after keyword, here and below
• { on same line, here and below

Forward decl is enough

Add license header

Newline after this line

Please use data-driven tests here.

This is a perfect fit.

See: http://doc.qt.io/qt-5/qttestlib-tutorial2-example.html

I'd suggest to build your own QProcessEnvironment (cf. QProcessEnvironment::insert, etc.), and pre-fill with values for PATH/HOME.

Then testing code gets easier, and you can use plain strings.

Add license header

What do you mean? Removing this line brakes the build with error "QProcessEnvironment not defined"

class QProcessEnvironment; here

Remove space

Nitpick: No space after identifier.

Newline before and after.

Please avoid overlong lines, hard to read in the diff viewer already.

... << ProcEnv{
    {key, value},
    {key, value}
}

Nitpick: Use a nicer formatting for the license :)

/*
 * DESC
 *
 * Copyright NAME
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public
 * License along with this program; if not, write to the
 * Free Software Foundation, Inc.,
 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 */

Newline before

"env" and "environment" isn't the best naming.
I would suggest:
env -> userEnv
environment -> sysEnv

Will fix. Thanks

I accidentally pushed a WIP patch anway (thus all the qDebug calls...). arc fail.