A preliminary question would be whether or not you want the two journals to know about each other. A single OJS install will share its user base, and that shared user base is probably the biggest factor in determining if you want one installation or two.
If you want one installation, in a multidomain configuration for OJS you will probably have an Apache virtualhost for each domain, and the mod_rewrite configuration will probably live there. “Out of the box” (without mod_rewrite or similar), you can configure OJS with multiple base_urls in config.inc.php, but they will need to reference the journal shortname in the URL, which is usually undesirable:
http://journal1.domain.tld/index.php/journal1/index/
and
http://scholar.domain.tld/index.php/journal2/index/
(In this case, the index could be available from both http://journal1.domain.tld/index.php/index/index/ and http://scholar.domain.tld/index.php/index/index/)
With mod_rewrite, see a similar conversation here:
OJS will register DOIs based on the base_url overrides (or, failing base_url overrides, whatever the currently accessing URL is), so there is no special setup to that.