Here are your parts
Replacement parts for WHIRLPOOL RH4730XDZ0 | AppliancePartsPros.com

Here is a wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%20883171.pdf

Do I need to replace the switch?
Cannot say. You would have to check the switch with a meter.

Does anyone know if the bulb holder is part of the replacement mechanism?
Looks like the bulb holder is a separate unit.

Also, how difficult is it to do all this yourself?
Should not be that difficult.

Also the first thing I would do is check that the replacement bulb you are suing has continuity. Would not be the first time that a bulb is no good right out of the box and ripping the hood apart to find out it does not have a problem is a lot of extra work.

Check the inside of the bulb holder to be sure the connections are OK.

Be sure to shut power off to the unit when working on it.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.