Would dark energy save the earth for a while as the sun heats up? Would the expansion of space (e.g. dark energy) move the earth further away from the sun over time, possibly saving us for perhaps a few billion years as the sun heats up?

Scientists now tend to think that the sun is heating up very gradually (e.g. over billions of years):
http://tvblogs.nationalgeographic.com/2010/07/21/hotter-and-hotter/

Dark energy is the unexplained accelerating expansion of the universe, as described here:
http://en.wikipedia.org/wiki/Dark_energy

Put another way, my question is, is dark energy working at such a rate that it would move earth (and other planets) further from the sun and prolong life on earth as the sun heats up?
I don't think this is a bad question, and I think Pela is essentially correct, the effect is very small.

Dark energy doesn't expand objects, for example, cause those are bound together, but dark energy should expand space between the sun and the earth though the effect is tiny.

If we take this number, 68 KM per second per 1 million light years (link below), that's 245,000 KM per hour per million light years or about 1 KM every 4 hours per lightyear.   With 63,000 Astronomical units per light year, between the sun and the earth, we can expect the earth (assuming it's in a perfectly stable orbit around the sun - which it's not, but lets say it is), a velocity of 1KM/30 years.   And that's over the age of the universe.   The earth/sun is only 1/3rd the age of the universe, so dark energy has accelerated the earth maybe 1 KM/90 years velocity since the formation of the solar system.   That's a pretty small push.  A velocity change of a bit a meter per year over the age of the solar-system.   The effect of the solar wind and the Jupiter and Venus orbital tugging are probably greater than that.

Source:  http://www.space.com/26279-universe-expansion-measurement-quasars-boss.html

Now, over a few billion years, a small velocity change of 1 meter per year would add up - so I think dark energy is part of the solar system's long term orbital calculation.  I might be wrong on that, but I think it has a measurable effect over billions of years even in distances as small as planetary orbits.   

But would it save the earth - I doubt it.  The sun's heating up accelerates over time.   It will at some point in the future, move too fast and get too hot for the earth, so, we'll have to save ourselves, either by moving the earth or terraforming mars, or building space colonies or some combination of all 3.   The good news, we have tens of millions, maybe hundreds of millions of years to figure that stuff out.   

Dark energy has been useful though.   It's probably kept us from crashing into Andromeda and/or the great attractor - however far away that is.   Certainly delayed those collisions (We're never going to crash into the great attractor, I gather, thanks to dark energy), and crashing into Andromeda, when it happens, might harmless anyway, but I'm just kind of thinking out-loud.  

I do think it's a good question as there probably is some small expansion due to dark energy between the earth and the sun.   If my numbers are wrong, I welcome correction.