There is no limitation to the REST API in SharePoint Online that would prevent you from filtering on a date. Without more details about the code and any errors produced, it is difficult to troubleshoot. Here's a couple things to check:
- When expanding Author, simply use the "Author" field, not Author/Id. Author/Id should be in your select parameter if you would like that returned. (E.g. ?$select=Author/ID,Author/Name,Author/Title&$expand=Author)
- If the "today" variable is set to "new Date()", your query will only return items created at the current second instead of the current day. You will need today's date without time in ISO format, and then use the greater than or equal to (ge) operator in your filter.
You can use the following code to set the "today" variable to the start of the day and format your query:
var today = new Date();
var RestUrl = _spPageContextInfo.webAbsoluteUrl + "/_api/Web/Lists/GetByTitle('XXX')/items?$select=id,Title,Body,Image,Created,LinkToArticle,Author/Name,Author/Title,Author/Id&$expand=Author&$orderby=Created desc&$filter=Created ge datetime'" + today.toISOString() + "'";
Hope this helps!