Pentium Ds are dual core chips, hence the "D". They're not true dual core designs though, it's basically a pair of Pentium 4 dies under the heatspreader. Celeron Ds are single core only though.
Actually, XP won't run on a 486 at all. Even if you install it on a Pentium machine and migrate it over, it still won't run. 486 CPUs are missing CMPXCHG8b and CPUID, which are required for XP to work. You can get XP to run on a 486 machine though if you install the 62 or 83 MHz Pentium Overdrive chip. I can't recommend it though because it's painfully slow, I know because I've done it before.
Another chip that XP might run on is the Cyrix Cx5x86, because that chip is essentially a gimped Cyrix 6x86. I can't test this though because I don't have one or a motherboard that would accept one.
Another hurdle you have to overcome is that you need 64 MB of RAM minimum if you want to actually install XP on the 486 machine, which many early 486 boards can't get anywhere near. Later 486 boards with PCI slots and 72 pin SIMMs can usually get up to this amount. I had a PC Chips motherboard that could go up to 256 MB (4 x 64M 72 pin SIMMs.)