1.5 min is just about the "dead time" of that size column at that flow rate (the elution time of any unretained compounds). What you're seeing is indeed "system peaks" (aka "t0 noise"; aka "water dip"). Ignore it.
That said, you really should not be trying to quantitate anything that elutes at less than 2x t0 (at least 3x t0 would be better). Your gradient conditions are *very* steep for that size column and flow rate.
The broad peak at the end may simply be due to the RI shift (unfortunately, UV detectors do respond somewhat to RI) as the surfactant re-equilibrates. It may also be due to additional proteins or other junk coming off after your gradient is complete. You can check by running the gradient and putting in a long isocratic hold at the end.
Another concern is the dwell volume (gradient delay volume) of your system. Remember that if you have 1.25 mL of delay volume (which would not be unusual), it takes a full minute for your mobile phase composition change to get from the pump to your column.