Here (native habitat) a 10 year old Joshua tree might be waist high. I'm not sure if that helps or not....and have no idea about root size.

Adrea

Joshua Trees grow very slowly and roots are short and shallow. Also be aware that they need very little water and, when older, can actually uproot if they receive too much. Take a look at the link below for more information.

Also, you might want to contact your state's appropriate agency to make sure you are within the law growing a transplanted Joshua. They are an endangered species and I believe they are protected in their native states (CA, NV, AZ).

Here is a link that might be useful: Yucca brevifolia information