Playing Ultimate DOOM and DOOM II Coop on Modern Hardware

With DOSBox you should have no problem

Here's a wiki

There you'll have some source port to play your favorite game :D

Note:

Doom requires a fairly fast computer to run inside DOSBox, but many ports of its source code exist for modern Operating Systems, so you may find more luck downloading one of them instead. Because Doom makes use of your sound card and potentially Modem, you should take care to match your dosbox.conf setting to the settings found in the SETUP.EXE found inside your Doom folder. For the most part the default options will work, but if you are making use of the Gravis Ultra Sound or MIDI audio devices you should pay special attention that the DMA, IRQ and Addresses all match.

Check out Doomworld's page on Windows source ports: everything from straight ports, classic-style ports but with modern networking, right up to the fancy-featured improved versions.

My recommendation would be Doom Legacy. It features some minor graphical improvements while still retaining the style of the original (stuff like transparent fireballs and support for modern resolutions), but it has extensive multiplayer improvements that should be perfect for you.