Palki and Doli are basically same. Hindus used Doli while Muslims used Palki in India, especially, in Awadh area of Uttar Pradesh.
Doli is simple and is usually decorated with ornaments and flowers while Palkki is roomier and has more intricate design with fine wood. the one my mom had was was stored in the far quarter of our house and which was later disposed of had sliding doors and was so beautifully crafted. i remember we used to play in there when we were kids. :)
Tera Mera Ik Jhagra, Alahh Aap Nabere,
Ve Lag Gaye Nain Awere,
Ranjhe Majhiyan Charaiiyaan, Doli Le Gaye Ne KheRe,
Tere Raah Ronde, Hanjhu Muk Gaye Ne Mere,
Jawan Sadke Mein Tere, Vehre Aa Varh Mere,
Tera Mera Ik Jhagra, Alahh Aap Nabere”
Tera Mera Ik Jhagra, Alahh Aap Nabere,
Ve Lag Gaye Nain Awere,
Ranjhe Majhiyan Charaiiyaan, Doli Le Gaye Ne KheRe,
Tere Raah Ronde, Hanjhu Muk Gaye Ne Mere,
Jawan Sadke Mein Tere, Vehre Aa Varh Mere,
Tera Mera Ik Jhagra, Alahh Aap Nabere”
I dont think so. I have never really been to a rural wedding, but I have seen marriages in semi rural environments but the doli is missing. It was there two generations back (grand parents). In some cases the middle class urbaners use it as a cultural thing (from outside the wedding hall to inside it).