Estimate Security level of the Rabin Signature
With proper choice of key and padding, the most efficient purely cryptographic known attack on Rabin signature and RSA (encryption and signature) is the same: factoring the public modulus. Therefore, size recommendations for the public modulus are the same. If 3072-bit RSA achieves 128-bit security by some criteria, Rabin does.

Beware that there can be implementation attacks specific to Rabin and its Jacobi computation, that do not apply to RSA. Also, Rabin signature is unforgiving to some poor padding (especially deterministic): it can degenerate into a total break (factorization of the public modulus), when it remains an existential forgery in RSA signature.