when i stared playing, i just healed. even when reaching endgame dungeons (not the hard raid stuff) i just healed. nobody ever complained about that. but after months of playing, getting down the job and game mechanics more and more as well as getting better equip, i actually started to dps on my own when there was no healing to do. there are times when there is no (unavoidable) real dmg on the group that a dot/fairy cant heal so why not add some dps instead of standing around

as said before, there is no need to dps outside of bleeding edge raid instances (and some rare dps races like odin final phase but at that time the boss just stands there and you have to kill him before he finishes his one-shot cast), so if you dont feel like dpsing, just dont do it. and if someone complains, ignore it. especially while leveling. your job description states "healer", every bit of dps is just a bonus from you.

also as been said before, if you absolutely dont want to dps, go AST, the class has the least dps potential but can buff the dmg of the group members with its card buff system (which is quite RNG based), so in almost every case you really just heal and buff with AST
WHM also is more on the healing side, but dont underestimate WHM dps