My Druid uses two clubs. Can I have the shillelagh cantrip active on both clubs at once?
No, shillelagh can only be active on one weapon at a time.
The shillelagh spell description says:
The wood of a club or quarterstaff you are holding is imbued with nature's power. [...] The spell ends if you cast it again or if you let go of the weapon. (emphasis mine)
It says the wood of a club or quarterstaff, which is only one. At the end of the spell description, it says this spell ends if you cast it again. So sadly, no you can’t dual-wield 1d8+Wis weapons at 1st level with no feats.