Might be better to get HP to push out decently coded Win8 drivers, because in all likeliness it will be your driver, not Windows
Now I have to wonder "which" Realtek gigabit adapter you actually have.
There are three known versions of the Realtek gigabit adapter - an OEM/semi-generic version (supplied to several OEMs, including nVidia and HP), the RTL8111D/E (also semi-generic, but supplied to several OEMs and IHVs, including ASUS) and the current RTL8111F. (The RTL8111D, E, and F are supported by Windows 8 directly - they all use the same driver, in fact - the earlier version uses a Windows 7-type driver.)
Also, you may want to grab Realtek's own drivers (yes - they actually DO write drivers themselves) as opposed to HP's drivers. (The rather amusing thing about Realtek's driver is that it is a generic, but WHQL-certified, Windows 7/8 driver for the RTL8111D and later - and it works with at least one NVidia LAN controller that I know of; the one included as part of the 630i nForce chipset.)
That issue is not one I've had (RTL8111E PHY), and I didn't have it with the nForce chipset after switching from nForce LAN drivers to Realtek's own drivers with Windows 7. However, if you are used to Intel PHYs and Intel Ethernet drivers (especially gigabit) you may likely be spoiled - I can admit to feeling that way (Intel PRO1000CT was the precedent to in terms of gigabit to the two Realtek PHYs I referred to).