You can do it easily if both iPads are on the same iTunes account.
You have two options, well maybe three.
1) You can use the Transfer Purchases option in iTunes on a computer to copy your music to the iTunes library, then sync the music to your other iPad from the same iTunes library. I don't recommend this if you normally sync the iPads to different computers. In that case, as long as both computers are using the same iTunes account, you can copy the music from computer to computer. More on this if needed.
2) You can open iTunes on the second iPad, open the iTunes app, select the Purchased tab where you will see all the music purchased on that account. Download what you want. There is a feature under Settings > Store that you can turn on on both iPads that will automatically copy new purchases to the other device; again, as long as they are on the same account.
3) There are third party computer programs that will copy your music off the iPad and on to another. I'm not familiar with any of them; so Google and buyer beware. This is primarily for those who hate and refuse to use iTunes; not always without good reason.
If you have two accounts it is possible to do any off these, but it means you'll be constantly be switching accounts in iTunes and on the iPads. If you don't keep close track of what was bought in what account things can quickly get confused. So I recommend that if you are going to share music/apps/books/whatever between iPads, you buy all that music on one account. Don't split it.