No.So to connect the 4060 output to the relay I need something like the one I have laid out below?
There's not sufficient current going to the relay coil, which likely is in the neighborhood of 150Ω.
You put the relay is series with the transistor collector such as below:
The 2N2222 has a maximum current rating of 800mA, which likely will be sufficient for the relay coil current.
The value of R1 should give a base current of about 5-10% of the collector current to fully turn it on.