Am I correct in thinking that offsetting Carbon emissions, (from burning fossil fuels such as aviation fuel), is as simple as planting trees? Can I plant my own?

Yes, that's correct. Though if you take your family on a long haul trip you'll need to have a very large garden :-)

For example, return flights from Heathrow to Orlando for a family of four produces nearly 8 metric tonnes of CO2. *An average 25 year old pine can absorb 6.82kg (15lbs) of CO2 per year.(* Approximate, as different tree species and trees of varying age absorb different amounts of CO2) For more information, please visit partners Climate Care, http://www.climatecare.org/ and use their emissions calculator to find out how much CO2 your family's holiday will produce and how to offset it by making a donation to plant trees. We would love to hear your views. Have you offset your family holiday emissions? Are you considering it? Sam at Take the Family

I don't know a great deal about it but there is a guide to offsetting carbon emissions here Carbon Offset / Carbon Offsetting - The Carbon Neutral Company

I must say the government has done a good job of making people aware of their carbon footprint and global warming. everyone seems to be talking about it.