When will my baby be able to sit in a booster seat at the dinner table?

6 months. Your baby can join you at the table now (in a bouncy seat or carseat), but they won't be able to sit well in a high chair until at least 6 months of age. It'll be even longer before they no longer need a high chair and it depends on how tall they are and how tall your table is.
Too big in highchair. A baby is too young to sit in a booster seat. Use a high chair until the baby is too big for a high chair, or until the baby is mature enough to stay seated in a booster seat at the dining table. Parents should teach a child good table manners by not feeding the child anything unless he is sitting nicely in a chair.
Able to sit. In my opinion, whenever he starts sitting up. It is okay to start a little early if they are able to hold themselves with support and have good control. Make sure all the restraints are fitted properly.
By 1, if not sooner. Babies can sit in a high chair usually by 6 months. It's a great idea to scoot baby up to the table to eat with you (first family meals!). There are small booster seats that hook onto the table which will support pretty small children and allow them to eat right at the table, even before they are stable enough to sit alone in a booster. A booster with a belt will be ok usually by 1.
Head control. Once your baby can maintain head control without flopping over, around 4-6 months, they can sit in a booster at the dinner table. Generally that also coincides with starting rice cereal, at 5-6 mo old. At first, it may recline a bit to give a little indirect head control and support, and as they age a bit, they can be sat upright to fully engage with those at the table.