Should I buy a DSLR instead of a digital compact camera?
It depends entirely on your needs and budget.
Many of the digital compact cameras come at attractive price tags theses days and have travel/family-friendly functions that are sufficient for most people.
DSLR cameras tend to have higher quality sensors than thus they produce better pictures with better image quality than the former. They also allow for more control with their manual settings and changeable lenses. Still, such control comes at a higher price tag as such cameras usually go from S$900 upwards.
Good in-between options are digital compact cameras that have manual override functions. Consult your photography retailer and find out more about these cameras that allow you to change exposure settings.