Hello Roger, The St Peter Anglican church in Liverpool has an entry which possibly could be your Joseph born 1860.
Thomas Joseph Moorhouse baptised 28 Jul 1861 son of Thomas and Isabella Augusta Moorhouse. If this is your ancestor there are several siblings as follows:
Sarah Ann Moorhouse bapt 2 Sep 1857 Sarah Ann Moorhouse bapt 1 Jul 1860 (first one may have died an infant) Mary Elizabeth Moorhouse bapt 22 Aug 1867 Robert Ireland Moorhouse bapt 13 May 1868
There is an entry of Joseph Moorhouse baptised 10 Jul 1864 son of Joseph and Sarah Moorhouse, but it was less common for parents to wait so long before baptising their children but not to be ruled out entirely. Have just discovered this one in the 1881 census aged 16 so probably not yours! I have to hand every entry involving Moorhouse in the 1881 census of England but can't spot your man. Was he in England at the time or am I assuming where I shouldn't be? Liverpool was a stepping stone to the outside world in the 1800's. Hope this is of use Cheers Mark E. Moorhouse