If you haven't moved before April then yes accept the place offered for the application made from your current address.
As soon as you have a new address, submit an application with the new local authority.
If you're in England, most schools don't have 'catchment areas', spaces are allocated by criteria eg siblings, medical or social need, looked after children, distance until all places are filled.
Popular schools can have very small intake areas, while less popular schools can be undersubscribed.
So how far away the school could be is impossible to answer until you have an address. If allocated on distance, the LA will offer the nearest school with a place available.
Something similar happened to a friend of mine. She moved in June and there were two schools with places fairly near. She choose one of them, put her child's name down for a closer school that she preferred, and moved her in Y1 when a place became available.