As @Martin Bonner has already answered, a "signed piece of paper" would merely be an evidentiary record of any contract into which you have already entered. Should you ever need to prove the terms that have been agreed, such a document would be useful—but is not strictly necessary.
Whether clear enough terms (for a contract to exist) have actually been agreed does, as Martin says, depend on exactly what was said and how such words would be interpreted within the local context. However, even if a rate of pay was not clearly specified, Remuneration Orders have been made in respect of many sectors and these may impose a minimum wage on the work that you are undertaking. In any event, it would be sensible to confirm how much you are to be paid (not least because you might decide it is insufficient recompense for your time and effort).
It's also worth noting that Section 8(1) of Employment Rights Act 2008 requires employers to give certain employees a written statement of their particulars of employment:
Every employer shall provide to every worker engaged for more than 30 consecutive working days a written statement of particulars of employment in the form specified in the Second Schedule, or in such form, in French or Creole, as may be prescribed, within 14 days of the completion of 30 consecutive working days' service.
Since you have only been working there for 3 weeks, you have not yet completed "30 consecutive working days' service" (whatever that means—"working day" is unfortunately not defined in the Act) and therefore this legal duty to provide you with a written statement of the particulars of your employment within 14 days of such completion has not yet arisen (though there is not, of course, anything stopping them from providing you with such a statement before the legal duty is imposed).
I am not familiar with Mauritius employment norms, but perhaps the fact that the law allows for such statements to not be provided to employees until they have been engaged for 30 consecutive working days is indicative of such delay being common practice? In which case, you might (as a practical point) find that any demands you make for a written statement prior to that time are received badly and cause friction in your relationship with your employer. As @Greendrake has suggested, you may wish to ask about these (non-legal) aspects on The Workplace.
Finally, it's worth considering why you want this document at this time. If it is to obtain clarity over your rate of pay, then merely seeking verbal confirmation may suffice? If it is to obtain evidence of the terms of your employment to protect against the possibility that your employer is acting dishonestly and does not intend to pay you at all, then beware that merely having the piece of paper is unlikely to have much impact: you will probably find yourself having to accept your lot or take them to court irrespective of whether they put anything in writing.