Hi Leon and welcome to the forum,
Plenty of people trade online without having a registered business, but you always have to be aware of any tax liabilities that may be applicable. Regarding suppliers, as a general rule, wholesaler's certainly won't deal with a non-business entity and while some dropshippers will, it is becoming common place for them to also require a tax id to open accounts also.
So yes, possible to trade as you are, but it does limit your supply resources to a degree.
Cheers