If you have any budget at all, I think a small gift is a good idea. Generally I don't think gifts "travel up" but this not really about work, its about creating personal goodwill with the whole office, especially the boss. A cute onsie and a rattle, or a set of bibs, can probably be obtained for $5, and if you have a stash of lovely wrapping and ribbons, it can make for a perfectly acceptable gift - its something that will get used. This really is a "its the thought that counts" type situation - it doesn't matter what you get, that you got anything will be appreciated.
And if you have no budget, perhaps doing more on the organizing side. Helping out will help you to better learn co-workers names, how various departments work (securing a conference room, coordinating catering, working with facilities for decorating, etc) since those procedures vary in each office, and involve a lot of grunt work. That type of effort is well received and often noticed and a perfectly acceptable contribution from a lower staff member.