"это легче и дешевле, чем идти в библиотеку"

Does this translate as 'it is easier and quicker, than going to the library?'
Or do I need to use a gerund instead of an infinitive? идя или идти?

Yes. It is the perfect translation.

A noun - поход  or хождение - would slighly change style and meaning.

идя is not a gerund. It is a part of speech we have in Russian. It doesn't have an English counterpart. You may call it "adverbial participle" or in any other way, different authors translate it differently. It is used when two actions are simultaneous, like

"thinking about her, I didn't notice...."

Here 'thinking' is like an adverb: it tells something about 'how' (or 'why') you "didn't notice", or just that the two things happened at the same time.

"это легче и дешевле, чем идти в библиотеку"

= 'it is easier and cheaper, than going to the library'

infinitive works fine in this case, or you could also use a noun "поход в библиотеку"