With most airlines, infants who travel and don't occupy a seat are still given a luggage allotment.
The disclaimer here is of course that not all airlines are considerate enough to accept items for your infant as a separate free allotment, and should you have further questions especially if traveling on a low cost airline, then contact them directly. The free allotment described in this feature are usually offered on airlines that are not principally classified as low cost or charter airlines.
Even though you may not have purchased a separate seat for your infant, you can check in luggage for the infant. In addition to your own free baggage allowance, the infant is entitled to one checked piece of luggage that is usually permitted the same weight allowance, or close to it, as if the infant was in a purchased seat.
In addition to a checked piece of luggage, the following items are usually accepted without charge as long as no items such as toys and clothes are teeming out of them - baby/car seat, bassinette, and stroller. Note that baby beds are not included in that list and would be considered excess baggage if you have already checked in your luggage limit.