Immersion when making early Shabbat might take some extra logistical planning. You should confirm in advance that the mikveh will in fact be open after your meal; in some communities you may need to make an appointment. You may also want to do some preparations in the morning to be sure there is time for them.

Aside from the concern about getting items stuck between the teeth, we are not aware of a halachic concern with immersing after the meal. If you are immersing after the Shabbat meal, you may eat meat and chicken so long as you take extra care to keep your teeth clean. You will need to clean your teeth in a manner permitted on Shabbat and wash any remnants of food from your hands and face prior to immersion. As with any immersion, you will do a final inspection (iyun) at the mikveh just before you immerse.

Alternatively, your husband could go to the early minyan and come home to babysit, but you could delay the Shabbat meal until after you return from the mikveh.

The timing of the tevilah should usually be after nightfall. In some communities, immersion may be permitted after sunset on Shabbat, when necessary. Speak to a local rabbi if this might be important in your case.

Please review our article on immersion on Shabbat and Yom Tov for further discussion of the preparation and immersion in this situation.