Considering GDP was first developed in the 1930's I don't think you will be able to find that specific information pertaining to the 19th century. I would imaging some people have gone back and calculated such figures but it would be incomplete information in my opinion. Unfortunately I don't know of any resources to find figures for military spending during that period. Maybe an alternative question would be... what methods where used during that time period to track economic growth and how does that correlate with our current understanding of economies? More specifically, what indicators did they use to justify economic policy or business decisions and where they as effective as what economists now use?

This site would be a good start. It will let you look at values for GDP from the time period but I would look at growth rates and purchasing power. Unfortunately I think this site is limited to the US, UK and AUS.

I don't recall if it matches up exactly with what you're asking for, at least for this period, but Paul Kennedy's The Rise and Fall of the Great Powers would be an excellent source. It contains plenty of tables of economic indicators, and hopefully you'll be able to find what you need.