IMac – How to transfer music betwen Mac’s

Yes it is, if you've set up the iTunes libraries for home sharing. Turn on iTunes on the machine with all the music. Go to iTunes on the machine you want the music on, then open look for other iTunes libraries on the network. If you don't see share libraries you may need to update the menu options in the General settings. Browse to the songs you want highlight them then click import in the bottom of the iTunes window.

I use this all the time to move songs, movies, TV Shows between my main desktop with a few TB's of storage and the different laptops around the house. This also works between OS X and Windows environments since it's connecting with iTunes.

EDIT: You can also configure the main iTunes library to automatically sync songs from the other libraries. This would mean that you only need to hook up a monitor once to set up the share the first time. You could also use this time to set up a VNC client on the main machine from which you could access the computer with your laptops and make edits as needed.

The iTunes store has a 'Purchased' section that you can use to view and re-download purchased music.

Open up iTunes on your computer and select iTunes Store in the sidebar. In the iTunes Store homepage, click the Purchased link in the Quick Links box on the right:

Once on the Purchased page, select the Music tab on the left and the 'Not on This Computer' tab on the right. Select All Songs in the list on the left and click the Download All button at the bottom of the page.

Once your downloads finish you should have all your music in your library, ready to be synced to your new iPhone.