If you have taken a plea which has a sentence
of probation, as a general rule, a judge will consider terminating probation early if a probationer has finished at least half of his required sentences, owes no fees, fines, or restitution, has completed all special conditions, and has never been violated during the course of his probation. At that point -- especially if probation agrees that he doesn't need them any more -- he can petition for the early termination of his probation.
As for being able to live with your girlfriend and her baby, the Department of Probation assesses each defendent and comes up with conditions and restrictions based on how likely the probationer would be to reoffend. If your girlfriend, for example has a criminal record
, a standard probation requirement is that a probationer keep company only with those who have only lived a law abiding life. Probation would also look into the facts and circumstances of your previous offense to decide whether it would be a good idea to let youo live with your girlfriend. If they decide against it, you could then go before the judge who has the ability to overrule probation. I cannot tell with a certainty whether probation and/or the judge will allow you to live with your girlfriend, but if her record's clean, it looks possible.