Can my old employer do this because there is a non-compete law here?

Any attorney advising you on whether your previous employer can prevent you from working for or starting a competing dog-walking business will need to review the actual contract that you signed with your employer. Its that simple. Given that I don't have the actual contract to review, the law in California is that agreements in restraint of competition are pretty much not enforceable. But there are EXCEPTIONS to this RULE-and your contract might contain one of those exceptions-so be careful! Two common exceptions (to a non-compete clause being unenforceable) go to the scope of the actual limitation. If the non-compete clause is limited to a locality where your ex-employer's business is located, or is limited to a shortened timeframe, these may be held reasonable limitations and could be enforced by California courts. Again, be careful! My best advice for you is to get good legal advice as to whether the non-compete clause of the agreement you signed with your ex-employer is limited in scope enough to be enforceable in California. It's just impossible to say without examining the actual contract.