I was just looking at ranger animal companions and thought exactly what you did, that spider is OP and that it needs a short or long rest cooldown. in 5e i believe the animal companions have 4hp per ranger level so all would have 12 hp starting at lvl 3 when you get them which makes alot more sense
I kind of like the different types of animals with different HP totals. That being said having 12 HP sounds more like the power level where they should be. Maybe you just don't get the Bear and Spider until later.