About Quake being slow under dosbox: what version are you using,
and under what operating system?

About dpmi: dosbox doesn't need any dpmi host, but the game (Quake)
needs it. Search for the csdpmi (cwsdpmi) package on the net.

Quake 1.01 unpatched
WinXP Pro SP2

Download DarkPlaces and use that for Quake.

Quake 1.01 is really old. Last version for Quake was v1.08 or v1.09 IIRC. The official demo and full versions of Quake come with CWSDPMI .....

If that's the case I can patch it using 1.06 or 1.08, I have both.

I tested on other computer: no effect in speed ... And that darkplaces-thingy's site is very weird and it doesn't allow me to download from there ...

Quake v1.01 isn't slow. It works fine here. Use dynamic core and auto cycles.

v1.08 is the version supplied by the mission packs and 1.09 is the version of Windows/Linux ports.

One problem: I don't know anything about that dynamic core ...

Open dosbox.conf

Change core= to "auto" or "dynamic"

to dynamic
auto doesn't exist yet

Let's try ... By the way, is there a way to make auto cycle enabled via the conf ?

EDIT: found that yes, it can. I put it to auto

OH THANK YOU ! The game runs just like on a DOS-computer ! Perfect 😀

But, however, I don't hear any sounds

start with low cycles (3000)
and increase them when you reach the menu(ctrl-f12)

That doesn't work, tried before

did you run the setup of the game ?

umm ... Quake1 does not have any, and I installed the game normally from windows. Is that the cause ? But I installed the update from DOSbox

in my quake dir there is a setup.cfg
maybe remove that one and see if it works
game works here with sound effects. (not music, but that is stated in quake itself specificly)

and check the idl directory as well
also some configfiles

This is what Quake says:

Sound Initialization
Sound Card is UltraSound
Sound sampling rate: 19293
-
MSCDEX not loaded, music is disabled. Use "-nocdaudio" if you wish to avoid this message in the future. See README.TXT for help.
Press a key.

Version is 1.06 ...