Nyora kupfuurira kweiyi ndima - Mazhinji ezvinyorwa zvake anobva mushure mekudzoka kwake kuItaly, uye mashoma chete ezvinyorwa zvekusavimbika anodzokera kumashure pakugara kwake kuGerman. Mhando yake huru yaive ballet, zvisinei zvakaoma kuita mutongo pamusoro pehunhu hwekugadzirwa kwake, sezvo yakawanda yemimhanzi yake isina kupona uye kutonga kushoma kwekutsoropodza kubva panguva yake kunozivikanwa. Pakati pa1775 na1777 akanyora ballet nhanhatu, uye muna 1778 ballet mbiri dzeTeatro Comunale muFlorence uye opera imwe yeStuttgart. Muna 1779 akava concertmaster uye mutungamiriri paTeatro alla Scala, chinzvimbo chaakachengeta kwemakore 23. Pakati pa1783 na1788 akanyora ballet nomwe dzeLa Scala, uye munguva imwe cheteyo akanga ariwo concertmaster paPio Istituto de' Professori di Musica. Muna 1797, pasi pokugara kweFrance
, akanyora ballet yefuridziro yeRepublican. Muna 1802 akanga ari mutongi mukukakavadzana pakati pehutungamiri hweimba yemitambo uye orchestra. Muna 1803 akasiya chinzvimbo chake paLa Scala, kwaakatsiviwa naAlessandro Rolla. Baillou akafa muMilan muna 1804 uye akavigwa muCimitero di San Gregorio, yakaparadzwa pakupera kwezana remakore reXIX. Ballet yake yokupedzisira, "La disfatta di Abderamo", yakatanga kuratidzwa pashure pokufa kwake muna 1809. Vakawanda vevana vake nevazukuru vakava vaimbi uye vakashanda paLa Scala.