Battery dimensioning
The other option you have are 3-cell LiPo batteries. These tend to have a fully charged voltage of ~12.6V, with a typical voltage of ~11.1V. When fully discharged they will drop down to about 9V. All of that is within the spec of your computers input - you say it is tolerant of 9-15V.

LiPo's will be far lighter for a given energy density which is why they are frequently used in RC Helicopters and planes. For example a 6Ah LiPo weighs about 400g, vs the 1.2kg of the 2.9Ah battery in your link - twice the capacity, 1/3 of the weight!

The thing with LiPos you have to be careful of is to include protection circuits for over discharge - many have this built in - and over charge. Charging is usually done with a special balance charger to ensure all cells get an equal charge.