For the 2012 Haiti DHS,

The distributions of cooking fuel are:


So most urban fuel is charcoal and most rural fuel is firewood.

Type of place of residence (HV025) was used for urban-rural in calculating the wealth index. Place of residenc (HV026) indicates whether the area is in a camp or not.

/HV025
1 "Urban"
2 "Rural"
/HV026
0 "Capital, large city (without camps)"
1 "Small city (without camps)"
2 "Countryside (without camps)"
3 "Camps Urban"
4 "Camps Rural"

I believe that HV026 was generated from the country-specific variables:
/SHCAMP "Camp"
/SHREGION "Région de résidence"
/SHLOCAL "Cité\Ville\Rural"
/SHREGNEW "Région de résidence"
/SHLOCNEW "Cité\Ville\Rural\Camp"
/SHLOCNEW2 "Cité\Ville\Rural\Camp"
/SHLOCNEW3 "Cité\Ville\Rural\Camp"

Their categories are
/SHCAMP
1 "Oui"
2 "Non"
/SHREGION
1 "Aire Metropolitaine/ Reste-Ouest"
2 "Sud-Est"
3 "Nord"
4 "Nord-Est"
5 "Artibonite"
6 "Centre"
7 "Sud"
8 "Grand'Anse"
9 "Nord-Ouest"
10 "Nippes"
/SHLOCAL
1 "Aire Metropolitaine"
2 "Cap Haitien"
3 "Gonaives"
4 "Les cayes"
5 "Autres villes"
6 "Rural"
/SHREGNEW
1 "Aire Metropolitaine"
2 "Reste-Ouest"
3 "Sud-Est"
4 "Nord"
5 "Nord-Est"
6 "Artibonite"
7 "Centre"
8 "Sud"
9 "Grand'Anse"
10 "Nord-Ouest"
11 "Nippes"
12 "Camp"
/SHLOCNEW
1 "Aire Metropolitaine (sans camps)"
2 "Autres villes (sans camps)"
3 "Rural (sans camps)"
4 "Camp"
/SHLOCNEW2
1 "Aire Metropolitaine (sans camps)"
2 "Autres villes (sans camps)"
3 "Rural (sans camps)"
4 "Camp"
/SHLOCNEW3
1 "Aire Metropolitaine (sans camps)"
2 "Autres villes (sans camps)"
3 "Rural (sans camps)"
4 "Camp urbain"
5 "Camp rural"

So the wealth index should be tabulated by HV026 or shlocnew3 if camps are to be distinguished.