Hi Helen
Welcome to the forum. In case you are not aware your real name may be showing as your Forum ID, if this is the case then I recommend that you change it as soon as possible. See
www.benefitsandwork.co.uk/guides-for-claimants/faq/forum In answer to your question, the first thing I would do is check that DWP have received your form, make a note of the date, time and who signed for it, then phone DWP; 0800 731 0122 and ask if you form has been placed in the system.
There is a backlog with most departments at the DWP, I have come across a number of AA claimants whose decisions have been quite fast compared to PIP claimants, but again it does depends where in the country you live.
Gary