Can I get a visa to transit Dubai while I'm in Iraq as a tourist?

Firstly, a transit visa won't be applicable because you are driving through UAE and as far as I remember transit visas for UAE are arranged through airlines. Individuals are either sponsored by someone living in UAE for short/long term or multiple entry visas or they go for an individual visit/tourist visa.

Since you are a resident of a GCC country you can apply online for a Short term single entry visa– tourist( 30 days). However, keep in mind that this visa usually has a processing time so you should apply for it as soon as you can. Also, you can expedite the processing by paying 100 AED extra, you can check this out in the service fee details section.

A sample of the application is also available.

There is one added benefit if you are an Indian citizen and have a valid USA visa or a green card; then you can get a visa on arrival at an airport or a port. source#1 source#2

You can get a normal visa online anytime, but keep in mind it may take a few days (up to a week) to process it.

You cannot have two outstanding visas for Dubai though, so I suggest you apply for it as soon as you land at Najaf.

Your other option is to apply for a multiple entry visa valid for 30 days; but this usually involves having someone apply on your behalf from within the United Arab Emirates.