The Doctor didn't necessarily pull back right away, but she did look sad as the poor woman reacted in such a way. She hadn't intended to frustrate her, but she realized Irene was probably more independent than many others and the idea of needing protection was hard. The Doctor had meant plenty of people like that over her many, many years.
"Peter's right. It's okay not to want help, but sometimes we need it. I need it loads of the time, actually." She looked at Peter, her nose scrunched a little. "Most of us don't go through alone, anyway. Too much could happen."
Then she perked up. "I could go with ya! Or Peter. Maybe Carol? Think Carol would go?" She glanced at Peter then at Irene. "I mean, far as protection goes, she's probably the best. 'Cept maybe Steve. Big Steve. You'll meet him eventually, though."