I saw this post earlier, and my first thought was that the code posted here was not really that applicable to the issue at hand (it was, after all, scraping a Fourmilab page for a table that does not contain the object you seek, but only the "major" solar system objects, which, unless it is staying close to one of those objects, did not seem that applicable).
I installed several Astro::* modules, thinking one could pull the orbital elements from a source (such as the Wikipedia article on (486958) 2014 MU69 ("1110113Y", "Ultima Thule") to compute the position. While trying to get that to work, I ran across a reference in Astro::Coords::Elements to two sites to obtain orbital elements, http://cfa-www.harvard.edu/iau/Ephemerides/ (although that one no longer allows directory listing, and links you to https://minorplanetcenter.net/iau/mpc.html) and http://ssd.jpl.nasa.gov. When I looked at the latter, I found they provide a web interface (HORIZONS) to look up ephemerides (including the RA and DECL for a location for a particular time) for the object. Not necessarily doing-it-yourself, but sometimes an easier path can be a better one (for certain values of "easier" and "better").
Hope that helps.