It appears to be a bit on the noisy side, yes, but you can always expect noise from the headphone jack of the DMG. From what I understand the most of this noise comes from the headphone amplifier and there are two distinct noise source.
1) "Transistor noise". This is the noise inherent to all semiconductors in different degrees. This is white noise. Not much you can do in the way removing it.
2) Power supply fluctuations/interference. This is just my understanding of it which is hopefully correct. For various reasons, the internal power supply line can fluctuate slightly. This carries over into the headphone signal. When the power supply ducks slightly, so does the signal, and you end up with interference.
This happens because the DC/DC power converter can't always keep up the pace with the changes in load by the CPU.
It gets worse if the batteries are almost dry. (Get new ones, or recharge if they are rechargeable)
It gets worse if certain capacitors are dried out. The cause for this problem is usually dodgy components. Game Gear was notorious for this for example. This is not a known problem for Gameboys, but might still have happened for example if the unit has been stored in in a moisture.
It gets worse when power save mode is on in LSDj as that turns the CPU on and off all the time. In newer versions of LSDj, the power save mode is hardcoded to auto. That's what pixls is describing.
But this noise is always there to some degree in the headphone jack. In my experience, prosounding always gives a nice and clean sound, so I would recommend you to actually do that.