Yes, you can date after legal separation, as there is generally no law against it. However, some states have strict requirements for legal separation. For example, some states require a couple to live separate and apart in different residences before the court accepts their separation. Otherwise, dating while separated may be considered adultery and this may negatively impact outcomes if you ever pursue a divorce.
Other states may not have such restrictions on a spouse living under the same roof. But maintaining the rule of no physical or emotional intimacy between you and your spouse is crucial. You should further research what your state says on dating after legal separation or speak with a licensed family law attorney.