Lilli, I really don't think it matters who introduces solids first, unless you would be sad to miss that "first". If you especially want to do it yourself you could start on a Saturday. I don't think it will affect your DD at all though.

WRT supply, no I didn't have any supply problems at all. The body is amazing with it's ability to adjust. You will even find that your body will know that it's a weekend so you will be feeding more often. I had all the same concerns as you before I went back, but in all honesty it ended up being much easier than I expected.