Linda,
There's nothing stopping you from buying a car. Actually anybody can buy a car even if they don't have a licence. However only people who have passed their driving test and hold a valid licence are allowed to drive legally on the roads. In your case, because you have a provisional licence, you will need to be accompanied by someone who is over 21 and has had her licence for 3+ years (that's probably going to be your daughter).
After buying the car, you can purchase the
provisional car insurance which will entitle you to drive your car legally as a learner provided you are supervised at all times (see above for who can supervise you). When you get your full driving licence, then you can look into an annual car insurance policy and drive unaccompanied.