I am confident that you could check it in; though you might like to put it in an outer covering bag to preserve it from damage.
AMS is a very long airport (especially if going from the BA checkin to the BA gate), though small trolleys are provided air-side for carrying smaller bags and shopping.
You could consider taking it with you through security and then using it to get to the gate, and checking it in at the gate. You can ask the BA checkin staff for that.