There are ways to do what you like. However, because of the way data is stored at the DataDrop, the speed of the query doesn't really increase if you select a single "group" as opposed to the whole group.
The simplest example is to just wrap Dataset around a Databin. You can specify the date range here, which definitely will speed up the download time. Of course, this will download all of the keys used in the bin. The following evaluation took about 2 seconds for my bin.
Dataset[Databin[binid, {DateObject["Feb 2"], DateObject["Feb 14"]}]]
If you only want to get a single key (or list of keys), you can try something like this:
Dataset[Databin[binid, {DateObject["Feb 2"], DateObject["Feb 14"]}]["Data"]["MyKey"]]
However, this takes the same amount of time as the previous evaluation on my machine (your results my vary!). Also, in this case, you won't necessarily need to wrap the databin with Dataset. This will depend on what you want to do with the data.