When he sees Rose walking down the street towards him, everything else goes straight out of the Doctor’s head. It’s impossible, unbelievable, but she’s real, and he runs towards her.
He doesn’t see the Dalek.
The extermination beam just grazes him, but that’s more than enough. Gravely wounded, his body failing, his companions carry him back to the TARDIS.
He’s a Time Lord so he won’t die, at least not this time; he’s not out of regenerations yet. Still, he’s reluctant to let go of this body. Maybe he doesn’t have to. He shunts excess energy into his spare hand…