Yes, you need a day use permit to be in Quetico for the day and these (single day permits) are issued at the ranger stations (self issue when off-season - Oct to May).
For what you are describing the easiest thing to do is to get the RABC and a seasonal vehicle day use pass - your canoe is your vehicle. One pass per canoe, regardless the number of people in the canoe. The summer vehicle day use pass is $75 CAD ($56 USD) and can be purchased online now for the 2023. Link below.
Seasonal day use vehicle pass With the day use pass and the RABC you can camp on the US side (with your valid BWCA permit) and day trip into Quetico. I’ve done this on Crooked a few times.
If you want to fish in Quetico, including on the Canadian side of border lakes you need the ON fishing license and the outdoor card. There are rules for taking fish from Canada into the US and these are available when you get your fishing licenses.
Contact Quetico Park Superintendent Trevor Gibb by email if you have any questions. I’ve found him to be quite responsive and helpful on all sorts of Quetico questions.