I'm a little bit surprised that the baptism record itself doesn't state the name of the church or chapel where the event took place, but then again, these things happen.
Assuming this is a baptism in the UK that you're talking about, you could try putting the name of the curate in the general search box to see if you get any matches with Crockford's Clerical Directories, a few of which are on Ancestry. However, even if you find the curate in question, it doesn't necessarily mean that he was linked to the church where the baptism took place, as quite often visiting priests (or "officiating ministers") stood in for the regular priest if he was unavailable. You could be lucky though. :-)