Dobbin is an old-fashioned nickname for a farm horse, especially one that's plodding and patient. As workhorses, so-called dobbins performed heavy labor in the family fields, such as hauling or plowing.
In Shakespeare's The Merchant of Venice, Launcelot encounters his blind father after many years apart:
Launcelot: Pray you, let's have no more fooling about it, but give
me your blessing; I am Launcelot, your boy that was, your son
that is, your child that shall be. . . .
and I am sure Margery your wife is my mother.
Gobbo: Her name is Margery, indeed: I'll be sworn, if thou be
Launcelot, thou art mine own flesh and blood. Lord worshipped
might he be, what a beard hast thou got! Thou hast got more hair
on thy chin than Dobbin my thill-horse has on his tail.