See spoiler, which talks about both season 2 and season 3.
Season 2 spoiler
#1, his self-preservation instinct didn't go out the window. Just because he loved Rose didn't mean that he would willingly accept his own death. Rose was going to die. I doubt that there is anything like an atmosphere in the Void, so Rose was going to die. In Who Confidential, RTD (I think it was him) described her scream as her death cry.
#2, had the Doctor jumped into the Void, he would have had no way to get out. Once the Void had closed up so that there was no danger of his own death, I believe he would have immediately gone into the Void in his TARDIS to rescue her. Here's a timeline of the rescue of Rose. Let's say that the Void is opened at 1pm local time.
1:30:00 Rose loses her grip and starts falling.
1:30:01 Because of the way the 2 universes were so close to collapse, Pete actually hears Rose scream and jumps across the Void.
1:30:02 Pete arrives in time to catch her.
1:30:03 Pete and Rose jump back across the Void.
1:45:00 The Void closes.
First, note that I have come up with what I think is a plausible explanation behind why Pete showed up at the exact right time to catch Rose.
Now, let's assume that Rose got sucked into the Void. I think the timeline of rescue changes.
1:30:00 Rose loses her grip and starts falling.
1:30:03 She is sucked into the Void.
1:30:06 Rose dies.
1:45:00 The Void closes.
1:45:01 The Doctor makes a mad dash for the TARDIS.
1:30:03 While the Void is open, the Doctor materializes just at the point where she would get sucked in, catches her and immediately dematerializes. He doesn't materialize before she gets into the Void, because that would risk the return of the Reapers. It still sort of breaks a Time Law, but I think he would have done it for her.
Now, I have question about Blink.
"People think of time as a sort of straight line, but when you look at it from a non-linear, non-subjective point of view, it's more of a great big ball of wibbly-wobbly, timey-wimey... stuff."
In the conversation he had with Sally on the DVD Easter Egg, he read from a transcript in 1969. The conversation was transcribed in 2007, based on what he said in 1969. He didn't get the transcript until 2008. When was the origination point of this conversation?
Blink is brilliant in at least 2 ways. #1, it's brilliant as a stand-alone story. #2, if you buy the premise, then you have to buy into the idea of the Master being reborn in 2007 + 100 trillion years, yet coming back and affecting events on Earth before he was actually reborn. It all has to do with the wibbly-wobbly, timey-wimey stuff.
Remember when Sally saw the Doctor and Martha walk by the record shop at the end of Blink? What would be truly fantastic is, when Martha comes back in season 4, we see that meeting take place in whatever story is going at the time.
end spoiler
I have the Edge of Destruction, but not the others. I've seen most of An Unearthly Child and nothing of The Daleks.
Speaking of which I was watching some Who fan-vids on youtube the other week and something got my attention in the crucial part of Doomsday: If 10 loved Rose as much as has been hinted at - then why was he just holding on as Rose went flying towards the void instead of throwing himself after her? Pete crossing over and catching her at last second was just sheer random fluke, a second later and she would have been lost with innumerable Daleks and Cybermen for company, while the Doctor just looked on...I wonder what John Smith's take on the situation would have been...