I made a vow that I will slaughter a sheep for the sake of Allah once I am promoted in my job. As I indeed got this promotion, can I slaughter a goat instead of a sheep?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

You have to fulfill your vow in a perfect and complete way, as much as you can. A vow is something serious. Allaah Almighty commands us to perfectly perform everything, saying (what means): {And do good; indeed, Allaah Loves the doers of good.} [Quran 2: 195] Allaah Almighty also praises His righteous servants with the quality of fulfilling vows, saying (what means): {They [are those who] fulfill [their] vows and fear a Day whose evil will be widespread.} [Quran 76: 7]

In a Hadeeth, the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever makes a vow and is able to fulfill it, let him do so." [An-Nasaa’i and Ibn Maajah]

Consequently, you are required to slaughter a sheep in fulfillment of your vow. A goat is not enough as it is not considered a sheep, neither in the eyes of custom nor in the eyes of the Sharee'ah.   

In Ar-Risaalah, Ibn Abi Zayd, a Maaliki scholar said: "… He has to slaughter a sheep to be absolved of liability." Commentators on this book explained that a sheep (in such case) must be valid for being slaughtered as an Udh-hiyyah (sacrificial animal for 'Eed).

Thus, you are required to slaughter a sheep that is known to be as such by custom and by the Sharee'ah, whether it is male or female. A sheep lesser than what is valid for Udh-hiyyah does not absolve you of your liability.

Allaah Knows best.