Only the top panels on the cabinets are porcelain, so that means your door is baked on enamel paint. This is something you could do yourself if you have any skill with a spray can, but you're not likely to find Harvest Gold, so in order to match your cabinet you'll have to have the color custom mixed somewhere. There may or may not be a fee for matching the color and most places have a minimum quantity of one quart. Unfortunately you'll likely be shocked at how much the paint can cost. I just bought enough paint to do three shaded Harvest Gold cabinets and the two colors, hardener and reducer cost me more than four hundred dollars. But I live in California and our state laws may be adding to the cost.

That being said, if your dryer door will fit in your oven and you're not afraid to use it you can skip the expensive hardener and bake it for a couple of hours at about 220 degrees. That'll harden the paint all the way through, but now I've gotten ahead of myself.

Preval makes a handy little device for spraying custom mixed colors(google Preval sprayer) that you'll want to pick up if you're serious about doing this yourself. It's almost as convenient as a spray can, the only real difference being that clean up is a bit more involved.

I hope that helps.

Each paint manufacturer has books of color chips intended to match colors used by the various auto makers and appliance manufacturers. When you look through one of these books and find the color you're looking for the guy behind the counter can then look up the mixing instructions for it and prepare some for you. This works great when you're painting an entire cabinet, but when you're just painting the dryer door you have to wonder if the surrounding paint has faded at all over the years. If it has you could still end up with colors that don't quite match, though careful use of rubbing compound on the faded paint could possibly fix that.

I paint refrigerators, using a foam roller,  and RustOLeum. They turn out  decent.

Congratulations on finding that door Christina!

If you don't have any budget at the moment, you can try spray cans as it's the cheapest way, if you don't like the result, you can always sand it down completely and try again later with something more expensive. Some good quality paint cans are also available but can cost about $20. 

If you know someone who has an air compressor and a decent spray gun (for automotive repair), you can also buy a small quantity of urethane paint that matches your dryer (not all whites are the same!) along with some hardener and reducer. 

To get the correct match and gloss, I'd suggest that you bring your current door to an automotive paint store to have it matched (or they'll give you paint chips so you find something close yourself). It will be a bit too glossy but they also add matting additive.

That won't be in the $4.99 range of Wal Mart spray cans but...