Proof that Water Pets are supposed to have significantly increased health regen:

[Dolalin]

EQ Stratics class guide mentions the water pet's health regen multiple times:

water pets regenerate fast and with one heal after the battle you are ready to go on
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strong regeneration (water)
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The water pet’s high regeneration rate also amplifies the heal effect and its high damage allows it to last a long time against most mobs (combine this with its agility and it can often outlast an earth pet and deal more damage).
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A water pet with its high regeneration rate in this role works even better.
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http://web.archive.org/web/200008311...sive_pt1.shtml

Oh and mentions the poison resist too:

Special abilities (e.g., water pet cannot be poisoned and can hunt asps/spiders)