Great question Natali! Your car won't need a smog check if you place it under non operation status. It sounds like your timeline to request a non-op filing is spot-on too!
For others; you can only request a non-op 60 days before your expiration or up to 90 days after. When past 90 days, the non-op option is no longer available and the vehicle will need to get a smog check, or at least the vehicle's DMV registration renewal fees need to be paid; the vehicle is placed under RDF (Report of Deposit of Fees).
For more info on this, check out... California DMV Planned Non Operation - PNO Filing Online - CA