I would say that 600 for a level 65 is pretty good... if that is your goal. It depends on how you play/how you want to play.
To give you a comparison, my level 111 Druid heals for about 800 or 850, I think. I know a level 100 Druid that heals more than me. We have different play styles. No big deal.
[edit: forgot that I restructured my build. My heal is currently about 620.
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The number of your heal is of very little importance in the grand scheme of things. The most important thing to ask yourself is this:
Is my training partner/group tank dying a lot?
If the answer to that question is no, then you have no problem.
If the answer is yes, then you need to find the source of your problem.
Possible reasons your partner/group tank is dying:
1. You are trying to fight mobs that are too strong for you.
2. You aren't keeping them buffed with Bark/your Bark is too low.
3. Your heal is too low for your level to keep up with the damage taken.
4. You are fighting in an area with adds, which might mean you can't heal.
5. Your partner/tank has the problem (build/armour etc).
Personally, I see absolutely no problem with having a 600 heal at level 65. Your training partners probably don't have more than 2000 health... they might be closer to 1500 (don't really remember that level range, and irrelevant anyway, as it was Update 2 for me). If you can keep them topped up, there is no problem. If they are dying before your Touch cools down, the heal isn't the problem so much as the mob difficulty is.
Remember that numbers are only numbers. Here are two Druids:
Druid One - low Bark, high Touch. Heals for 900
Druid Two - high Bark, some Abundance, mid Touch. Heals for 700
I would argue Druid Two is more useful. Higher Bark will result in less damage taken (less need for healing), and as Touch is focused on a Tank, the high Bark can be cast on other group members while Touch is cooling down.
I would personally suggest you focus on getting some Wards rather than worrying about your heal. If you can pick those up through your main/clan, you will be laughing. Again... higher buffs and resists will mean less damage is taken.
Good luck.
Oh, and to Feathery... high score is not 1000ish. 1000 is run of the mill. I don't look at the online rankings, but other Druids in my clan heal 1400 or more. I think 1800 is the highest I have heard.