If you received a rebate when you installed your solar electricity panels, you can still move the system when you move house. You just have to get permission from the AGO first. They'll need proof of ownership of the new property (e.g. council rates notice), and proof that it's your primary residence (e.g. updated drivers license).
If you're selling the old property, make sure it's clearly spelt out in the contract of sale that you'll be taking the panels with you. Also make it clear that you may not be able to take the panels immediately because you will need to wait on the AGO permission and the tradesperson's availability.
I've found it is hard to find someone who can move the panels for you. Your best bet is to start with your original installer - this makes things like warranty etc simpler as well. If they can't/won't do it, then start looking for local electricians with solar experience.
Moving costs should start at around $1000 or so, but expect to pay more if the roof types are different (you may need new mounting brackets), if access is difficult (e.g. multi-storey building), wiring is complex (e.g. poor access to roof cavity, long cable runs), etc. You will probably need to pay the costs for the grid-connect hookup again, too - check with your local utility company.
I'm going through this process at the moment, and it does take some time. Not many people have done it, so it's all a bit of a learning curve for everyone.
Is it worth it? In my experience of trying to sell our old house, almost nobody understands grid-connected solar power (especially the real estate agents!). They eye it suspiciously, thinking they're going to be up for additional maintenance and repair costs down the track (they've all heard that batteries for solar systems are expensive - they never quite get it that there are no batteries in grid-connect!). Even when it's all explained, I don't think it adds any value to the house - nice to have, but not worth paying extra for. It wasn't going to get us a higher price, anyway, and this was a house in a fairly affluent area.
The cost of moving your system is certainly going to be less than the cost to purchase a new system for the new house. If your system is still relatively young, then you'll get a good long service life out of it almost comparable to a new system.
In summary, unless you have a buyer that understands grid-connected solar and is willing to pay extra to keep it, it's certainly worthwhile to move your system to your new home.