Tried it out on my Win98 machine as well as on DOSBox. I couldn't get DOSBox to work at 1600x1200. It complained about not having a compatible VESA driver for that resolution.
1280x1024, Win98SE, Celeron-1400, 440BX, Voodoo3 3000 AGP
Low: 33 FPS
High: 57 FPS
Average (walking around with no enemies on screen): ~45 FPS
1280x1024, DOSBox 0.74 on Win7, i7-4930K @ 4.6GHz
Low: 45 FPS
High: 140 FPS
Average: ~75 FPS
So based on that, I'd guess that DOSBox on a fast machine would be able to handle it smoothly at 1600x1200.
The 1.4GHz Celeron would probably average under 30 fps at 1600x1200, but I'm guessing that most P4s above 2GHz would handle it fairly well.
P6 chip. Triple the speed of the Pentium.
Tualatin: PIII-S @ 1628MHz | QDI Advance 12T | 2GB DDR-310 | 6800GT | X-Fi | 500GB HDD | 3DMark01: 14,059
Dothan: PM @ 2.9GHz | MSI Speedster FA4 | 2GB DDR2-580 | GTX 750Ti | X-Fi | 500GB SSD | 3DMark01: 43,190