Adding DME after adding yeast?

My OG was low and I'm thinking about adding some DME (boiling it in water first of course). I've already added the yeast though. I understand that I could risk contamination but if I'm safe it should be fine right?

It will be almost a full day since I pitched the yeast...

Should be fine. There are actually some recipes that call for adding additional sugars during fermentation. I would add it soon though.

Just boil it up in a bit of water, let it cool (covered) and add it gently and you should have absolutely no dramas.

I just did this last week, not once, but twice on the same beer. My Holiday spice ale has a 1.100 starting gravity. Rather than doing it all at one time, I have developed this recipe that starts at 1.080 and has two additional infusions of unhopped wort concentrate. (actually, to be honest, my extract efficiency was so low on this big beer that I had to come up with plan B after the fact)

I made the first addition after the Krausen has fallen on the 1.080 ale with 3lbs dme boiled in 2 qts of water. The fermentation took off again (this time requiring a blow-off tube it was so vigorous).

Once the activity had slowed on that second fermentation I added another 2 lbs of sucrose boiled in 16 oz of water. This fermentation was slower because the sucrose had to be broken down, but by this time the yeast population was at its peak and they devoured that sugar in no time.

This has worked so well that I have modified my all grain recipe over time to be more of a basic all grain brew with roughly 10 lbs of malt and 5 lbs of LME

RDWHAHB and if your hopping rate is no too high because your yield was low then your are probably better off by added more sugar to the brew.