I am assuming you are in the UK!
As previously mentioned a DIY will is perfectly legally valid. Just make sure that it witnessed by 2 people who are not beneficiaries and that it appoints somebody (you) as executor/executrix.
also, if the gross value of the estate is less than a certain threshold (currently �10K - I believe) and the deceased didn't own any stocks/shares or freehold land then a grant of probate is not needed (unless her bank is awkward, which some can be). The executor can simply dispose of the deceased's propertymoney according to the will.
I would suggest waiting 6 months before doing so, as that is the time limit for contesting a will (if there is anybody likely to contest it).
I would suggest you go to a bookshop and buy a book on proving a will. (WH Smith do a good one!)
This is exactly what I did for the estates of both my parents!