My rambling thoughts:
A nursing newborn is always an exception I see no problem with. Newborns are their own breed. But 7.5 months isn't a newborn anymore. Especially, as you said, she's gone back to work and does have the ability to have him fed w/o being there.
Although, I will say that pumping SUCKS and if it's more that she would need to pump during that time and it's easier to bring him - I couldn't say "no" to that.
The issue of it being that she doesn't want to be apart from her kid - eh, not a reason to say "yes". She will be faced w/ other "no kids invited" events in her life and if she just can't stand to be away, then she needs to simply RSVP "no" instead of putting the hostess in the position of telling her "no" the kid can't come.
As for what other people will think, I just don't care. Your friend asked for an exception, they didn't. And really, in the end, I don't feel a 7.5 month old will be all that distracting (at least if your friend has any tact about it!). I really just wouldn't worry about the other people. If anything happened to be said to you, just say "As she's nursing, she asked to bring him and of course I said yes".
Which brings me to my ultimate point - it sounds like you want to say "yes" and as such, say "yes".