Jors,
Our SOPs for a high level go-around state that first of all we level off, bring in one stage of flap and when in level flight raise the landing gear. Then we would climb or descend at a sensible rate to the published missed approach altitude and start accelerating to minimum clean speed retracting flaps as we go. As for the lateral profile, we have to ask what ATC requires or follow the published profile.
In the case you mention though, at only three miles out, we would execute a standard go-around procedure with go-around thrust.