Trying to transfer ALL of my data, including OS to new Macbook Pro using time machine

Hi.

I have two Macbook Pros, an older and a newer one, that had been used by another user.

The older one is beginning to fail, so I need to transfer EVERYTHING to my new one

This includes the OS.

I have already Erased the Hard Drive on the new computer, so it boots up asking me what I want to do.

One of the options is "Restore from Time Machine"

I do have a recent full backup on Time Machine (of my old computer)

And would like to use this option, as it would simply "mirror" my old machine...however...

When I select the "Restore From Time Machine" option on the boot up window of the new computer that has no OS on it, the next window warns me not to use a computer that was not the source of the backup. Should I do it anyway? or is there any other way?

My other choice is to buy an OS that I have already purchased, because of a snafu at the mac store, does not show my purchase, but truly it would be easiest in any fashion, just to transfer EVERYTHING Via Time Machine.

Any suggestions will be greatly appreciated.

Thanks