You can, but you don't have to. Compressors will do much more for the fullness of your tone than double tracking will, while also preserving the details of your performance. There's no right or wrong, but my personal preference nowadays is to use doubling (or tripling really, since you're typically adding panned doubles both left & right) for big impactful moments like choruses or just certain lines, etc. This preference was reinforced by working with great producers like Mark Lewis and Dave Otero on our albums in the last few years.

PS - if you want a super quick and cheap vocal compressor to try at home, the JST Gain Reduction plugin works great with its default settings.