Yes, you can do it yourself. Depending on your circumstances, you may not need legal advice. The Family Court provides kits for parties to apply for their own divorce, without legal representation. The kit is free. It has excellent, comprehensive information. Documents can be filled in by hand. The Form 4 application itself can be downloaded in PDF format from the Wikivorce Site.
There are two versions of the form - one for when there are children, and a shorter version if there are no children. You are however, strongly urged to get advice on ancillary matters such as child welfare and financial settlements.
For example, if you leave the home without the children, and then want to seek residence orders, the person remaining in the home will retain interim residence. This is on the basis that you left the home, conceding that the children were better off staying with the other parent. As a final hearing can be delayed for over a year, this could result in a permanent residence order to that effect. This would be different if you were forced from the home, for example because of violence. The message however, is very clear. You really should obtain legal advice before you actually separate.