COS from H4 visa to H1b visa

Hi ,I came to US on H1b visa worked for 5 months and later quit due to family emergency and currently I am on H4 visa. So now can a company(employer) file for a COS from H4 to H1b for me?My previously filled H1B visa expired date was Sept 2015.Will I come in the H1B application quota or no?