Is the Babadook symbolic of the dead father?

In short yes.

Although not exactly. The real symbolism behind the Babadook is the mother's grief over the death of her husband and her resentment towards her son. The movie is a metaphor for her internal struggle to reconcile that resentment and grief so she can give her son the love he needs. This has been supported by a number of different film critics and there is even a section of the wikipedia page for the movie which supports this idea.

Writing for the Daily Beast, Tim Teeman contends that grief is the "real monster" in The Babadook, and that the film is "about the aftermath of death; how its remnants destroy long after the dead body has been buried or burned". Teeman writes that he was "gripped" by the "metaphorical imperative" of Kent's film, with the Babadook monster representing "the shape of grief: all-enveloping, shape-shifting, black". Teeman states that the film's ending "underscored the thrum of grief and loss at the movie's heart", and concludes that it informs the audience that grief has its place and the best that humans can do is "marshal it".

Egyptian national film critic Wael Khairy wrote in his "Film Analysis" on 22 November 2014 that The Babadook "taps into something real, a real human fear". Khairy argues that what the Babadook "stands for is up for debate", but writes:

"The malevolent Babadook is basically a physicalized form of the mother's trauma ... I believe, the Babadook embodies the destructive power of grief. Throughout the film, we see the mother insist nobody bring up her husband's name. She basically lives in denial. Amelia has repressed grief for years, refusing to surrender to it."

Khairy concluded that the film is "based on something very real" and "feels unusually beautiful and even therapeutic."

Amelia probably wrote the book immediately after Sam's birth but waited several years to read it to her son. In a classic instance of dissociation, Amelia could have created the not-so-proverbial monster as part of an exercise in free association writing (and, in her case, doodling). Her statement to Sam that she "wished it were [him]" means the Babadook was a means of creating a psychological scapegoat, a standard case of "the monster made me do it". The reaction, upon having the book show up at her doorstep, followed by the menacing phone call, is a surefire example of Amelia's utter denial of her personal demons. She is the Babadook, lain and simple On a linguistic side-note, the Babadook is not only an anagram of "a bad book" ("bad" in the sense of "malevolent") but also the husband's/father's ghost using baby talk with Sam: dook dook dook being onomatopoeic for knocking, while baba meaning "papa" in baby talk and "dad" in Mandarin Chinese.