What follows "to" in a noun clause is a gerund (verb+ing), making "working" the correct choice. The sentence is a negative statement ("not so well disposed"), so the tag question should be positive. Since "are" is the auxiliary verb in the main clause, the correct tag question is "are they?"

Thus, the best option is:
"A number of doctors are not so well disposed to working in government hospitals these days, are they?" ✅