There is no hard-and-fast rule for headphone jacks; be it a laptop, MP3 player or a regular stereo system.
I would say that a typical headphone output adheres to Line Level specifications, although for headphones they become more of a guideline than a stringent set of figures.
As you have already discovered, different devices have different output levels.
The power that can be provided by your PC is, for example, X milliwatts. As the PC power supply can give up 12V to the soundcard, the XmW could well be generated with an emphasis on the voltage rather than the current. Some top end motherboards (the latest Asus ROG boards, for example) boast a headphone-jack output of over 2V rms.
A portable MP3 player may only have a 3.7V lithium battery. Its output power could be the same XmW as the PC, but at a lower voltage therefore higher current - without some boost convertors it would be impossible to match the voltage of the aforementioned high-end motherboard.
A fundamental difference between a 'headphone output' and a 'line out' is that the latter isn't designed to power a low impedance load. I tend to assume that the input impedance of a generic audio device to be 50kOhms; if it's ever critical to know then it's typically stated by the device manufacturer. Headphones or earphones can be as low as 32 Ohms, meaning that plugging headphones into a Line Out socket could result in both poor volume and poor quality. There is not generally the same problem with connecting a line-level device to a headphone output unless you consider a dedicated headphone amplifier; an audiophile might argue that the output would become unbalanced.
Thus there is no correct answer. Perhaps start with 1.4V RMS as a maximum and then increase or decrease as you work through your prototype.