Awesome idea. I would love to see those benefits tied exclusively to a perk tree, without the incremental increases on level up. Otherwise even if I'm ignoring hand to hand and playing as a mage I'd still be getting faster and jumping higher with each level up. Maybe that was your intention and I read the post incorrectly. If so, I apologize

Here's my 2 cents on the abilities:
1) Stamina Regen - Great idea for a monk class, but I'm not sure about the ratio. If 100% is double normal speed then that might be fine, but I play as a Redguard and their racial for stamina regen is absolutely insane.
2) Unarmed Damage - As others have said, you'd need to make sure this is balanced. I'd suggest making it the first perk in the tree, with 5 ranks at +20% each, just like the Blade and Blunt trees.
3) Movement Speed - Awesome idea, and something that would definitely appeal to me as a player. 50% faster would be a great perk in the top half of the tree.
4) Health Regen - Same as stamina regen. So long as it's balanced I'm all for it. Certainly makes sense for a monk to have this.
5) + Armour - Only if you can ensure this effect only applies while unarmoured. I think there's a perk in the Alteration tree with this requisite, so it should be possible.
6) Jump Height - Nice idea, but double is a little too high I think. Jump height is believable for the first time in this series, so any more than 50% higher jump height would detract from that realism I feel. Still, would be a useful perk for those few dungeons requiring acrobatics, so it could be nice as a lower tier perk. I don't think it would be useful enough to warrant taking up a higher tier perk slot though.
Extra Suggestions to Consider:Other members have already suggested hand wraps as weapons, but I'd love to see that extend to
leather knuckle dusters and claw weapons like the http://www.freewebs.com/norstar1/1Medieval_Katar_M.jpg, for example.. That gives the monk class a reason to invest some time in Smithing, and avoids some of the issues fists as a weapon had in previous TES games (no improvements in quality such as iron/steel/elven for damage boosts, and cannot be enchanted). Would also allow for some extra visual flair in their design.
Meditation - Something akin to Geralt in the Witcher, but without potions. Before entering a cave the monk could choose to sit down and meditate for a moment or two, focusing his inner spirit or chakra. This would lead to a buff being applied (depending on the meditation) for the next 10 minutes or so. You could have various meditations for different situations, allowing the player to choose between a boost to damage, to magic resistance, to armour rating, to stealth skill, to attack speed, and anything else you can think of that would add variety and options to play style. It adds something unique to the class, to differentiate it from the others. Perhaps meditation should be unlocked in the perk tree to prevent everyone having access to it regardless of whether they play as a monk or not, or perhaps it should be as a quest reward for a monk-focused storyline. I'm not sure.