6 weeks is a good head start for tomatoes, so I would say definitely you can wait until you get back to start those. Peppers take a bit longer, so you may want to start them now. I've never done eggplant, so I can't speak to that one.

It is always best to be there to monitor them. Even if it means you wait and plant out a bit later. And planting out a bit later than planned is often a good thing.

I am not sure what your zone is but what I have learned with tomatoes and peppers. Is to wait until the ground is near 60 degrees for a few days. Otherwise your plants can end up in shock. Plus you should harden them off some.

I'd wait. Much higher chance of success when you are home taking care of them. You have plenty of time to work with.

I'll wait, thanks for the advice!