Wikipedia offers a formula (from a paid-for source, here) for estimating the time to tidal locking for two given planets. (See Tidal Locking Timescale.)
$t_{lock}=6(a^{6}R\mu)/(m_sm_{p}^{2})×10^{10}$ years.
Masses in kilograms and distances in meters.
For your earthlike worlds, $\mu$ can roughly be $3×10^{10} N·m^{−2}$.
$m_{p}$ is the mass of the planet
$m_{s}$ is the mass of the satellite
$R$ is the mean radius of the satellite
$a$ is the semi-major axis of the satellite around the planet. (The square of the orbital period of a body is proportional to the cube of the semimajor axis of its orbit.)
The formula assumes an initial 12-hour rotation period. (However, a more cumbersome formula exists on the linked page for calculating tidal lock time for different rates of rotation. 12 hours seems like a reasonable value, however, primordial Earth probably had a rotational period of about 6 hours, so there's room to push things.)
Plugging the values you've given for masses and orbital distance, we can estimate:
... that the double planet will tidally-lock perhaps 12 million years after formation. (The planet loses on average 0.0036 seconds of its day per year.) There are many factors that can contribute to error in the formulas. Wikipedia states that in some cases, they may be off by orders of magnitude.
It's important to note that larger satellites tidally lock themselves faster than smaller ones. Mass $m_{s}$ grows with the cube of radius, and so does the mutual attraction.
A possible example of this is in the Saturn system, where Hyperion is not tidally locked, whereas the larger Iapetus, which orbits at a greater distance, is.
