Your plan is a clear case of preconceived immigrant intent, which she is not supposed to have when entering the US with a tourist visa. If they realize at the port of entry that she has a US citizen child who is an adult, they could refuse entry because of suspicion that she will file for AOS.
You should file I-130 for her now with the Consular Processing option. That avoids the immigrant intent and refusal of entry problems that may result from it, and she would get the green card sooner that way. Instead of entering in September to start the GC process which will then take until December or January or February, if you file the I-130 now she would probably get the immigrant visa at the consulate by September or October. Then once she lands in the US with the immigrant visa, she is a permanent resident.
Very good advice..this is why I love this forum.