It's too strong. Way too strong. A 108hp buffer every short rest at 2nd level is borderline broken. It invalidates the fighter, and outclasses every other class feature gained at that level by the other classes. It makes encounter balance really wonky too.
The fighter only really catches up to the Druid at 11th level and at that stage the Druid has 216 bonus hit points per short rest from elemental form.
And I don't even want to get into the moon Druids capstone at 20th that makes him all but invincible.
I've found that simply ruling the Druid to retain his own HP and HD in wild shape forms removes this unbalance. Granting the Druid temporary HP equal to 2 times his Druid level grants a nice buffer while in animal form, and is approximately on the same level of power as other class features (lay on hands, second wind etc) gained at that level by other classes.
It also avoids 'onion Druid' cheese.
The low AC of animal forms is only an issue at 2nd level (when the Druid gains the ability). He still gets 4 temp Hit points, 2 attacks a round in bear form doing a ton of damage at the same attack bonus as the Fighter (if not higher). He can also burn slots as bonus actions to heal while in wild shape remember. That plus the temp HP makes him still be a damage machine and be able to soak as much punishment as the fighter - if not more.
At 3rd level, he gets bark skin, so the AC problem is ameliorated.
It's balanced the classes quite well. Even with the house rule, moon Druids are still scary - just not wildly OP.
Also moon Druid 2/ barbarian 1 can soak about 260 hit points per short rest thanks to Rage and wild shape hit points. That's an obnoxious amount of damage to plan for and it trivialises most encounters of that CR. As a DM you can plan for it by upping the CR of your encounters, but then you face a TPK if the Druid goes down.
Finally, all this house rule does is make the Druid about equal to the Fighter for most of his career; maybe a little behind in terms of raw DPR and feats/ manoeuvres in battles. Considering the versatility of wild shape and the fact the moon Druid is sitting on a full casting chassis, it balances the classes out nicely.
1) The CR 1 Brown Bear (moon druid wildshape from level 1-5) has 34 HP, not 54. The Dire Wolf (Also CR 1) Has 37 HP, and the CR 1 Giant Hyena has 45 HP.
Yes, in the early levels, moon druid wildshape easily outclasses others.. but this drops off very quickly. They are stuck with the same forms until level 6 - and the level 6 (CR2) forms are not much of an upgrade.
2)Elemental wildshape consumes both uses of wildshape.. so 1 elemental shift per short rest. This is only effectively doubled vs. non magical weapons.. but we are talking level 10 here.
Barkskin helps, but don't forget it requires concentration. AC 16 is still not great..a lowly kobold is hitting on a 12, not even counting pack tactics.
In my experience thus far, the druid wildshape is amazing up until around level 5.. currently at level 6, enemies are dropping the druid out of wildshape in 1 round of combat, or just ignoring it entirely. Flying enemies make bears.. well, sad pandas
Wildshape suffers from some other issues.. no casting while wildshaped, no benefit from magic items while wildshaped, and a large lack of scaling/synergy with feats.
Again, I do not disagree that wildshape is out of line early on, I only stated that it tails off as levels get higher.
I think temp HP is a good idea (Though 2x druid level is on the low side, imo... at level 2, that is 1 average kobold hit) I would also consider scaling the beasts other statistics- use the druid's proficiency bonus+the applicable combat stat from the beast, rather than the static value. (ex: level 3 druid, shift to brown bear- str 19. Melee weapon attack 2+4=6)