There are three significant symbols in this brilliant play that are worthy of attention. The first of these is Thea's hair, which is shown again and again to be abundant and beautiful, especially in the way that it is contrasted with Hedda's hair. Note the way in particular that Hedda seems to be obsessed by Thea's hair. This was one of the things that she hated about Thea when they were at school together, and it continues to be a point of annoyance for her during the play. The reason is of course that Thea's hair symbolises those feminine qualities that Thea possesses and Hedda lacks.
The pistols that Hedda plays with are recognised as being symbols of masculinity. George Tesman and Judge Brack are both shocked and surprised that Hedda plays with them, and some critics have suggested that the pistols are actually phallic symbols. The way in which the pistols are related to Hedda's character suggests a masculinity in her being that is a result of the way in which she has repressed her more feminine instincts. They could also be said to symbolise the freedom that Hedda so eagerly desires but is unable to attain.
Lastly, you might like to think about Lovborg's manuscript and the way that in a very real sense it symbolises the child of Eilert and Thea, as it is birthed through their mutual love and affection. Of course the act of Hedda in destroying it is very significant, as she is jealous of something that she, through her attitude and character, is unable to participate in or enjoy.