Is the 'eternal covenant of redemption' biblical?

Yes, very biblical, very Catholic, and very true. Hebrews 9:15 uses that very idea, speaking of Christ as the mediator of a new testament so that those called may receive the promise of an eternal inheritance, or as other Bibles render it, eternal redemption. It means the whole thing was planned out and predestined from the beginning; God did not wake up one day after Adam and Eve sinned wondering what to do. From beginning to end it was all understood, and yet man still has free will, which seems impossible, but that is the antinomy of predestination and free will that Scripture presents; it is not predestined in the sense that man is a puppet. In Acts 2 Peter tells the Jews that Christ was delivered up by the foreordained plan of God, and yet they killed Him by their own free will; in the Greek those words for foreordination are as strong as they could be. Now notice the word 'inheritance': Hebrews goes on to say that where there is a testament, the death of the testator must occur for the will to take effect, just as with any will your parents make. So the New Testament requires the death of the testator, God in Christ, for the inheritance to be received by us, the beneficiaries, and this was even partially true of the Mosaic covenant, where the death of animals in sacrifice, signifying the death of the testator, was required so the people could be even partially forgiven. It all leads to Christ, the perfect sacrifice, whose death releases the inheritance in its fullness to all who are in the will.