Trump is slightly ahead of schedule according to the reporting of 538, which relies some on the Washington Post:link:538 blog
There have been numerous news reports of disarray in Donald Trump’s presidential transition process. But by selecting Jeff Sessions to be his attorney general on Friday, Trump made his first Cabinet pick at an earlier date — Nov. 18 — than most of his immediate predecessors as president-elect. According to The Washington Post, just two of the 70 Cabinet picks by newly elected presidents since 1980 had come by that date, both of them by George H.W. Bush.
Ed Update, as of Jan 20, Trump has slumped:
In all, Mr. Trump has named only 29 of his 660 executive department appointments, according to the Partnership for Public Service, which has been tracking the process. That is a pace far slower than recent predecessors, falling far short of the schedule originally outlined by Gov. Chris Christie of New Jersey, who was Mr. Trump’s transition director before Mr. Trump ousted him 10 weeks ago.
As you can see from the above reference, it's perfectly normal to begin naming appointees. There are a lot of them. Please see the Plum book for a full listing.
Presidential picks that require Senate confirmation will not be reviewed and voted upon by the Senate until the new Senate and President are sworn in. White House nominations and appointments are recorded here White House
The process can take awhile as there are about 1000 positions and the confirmation process is very onerous Slate
And the Congressional Research Service found that Obama had over 1/4 of his positions vacant 1.5 years into his second term FCW. Your question on how long it usually takes is that no one really knows for sure.
And because the number of presidential appointees changes from one administration to the next, it's especially difficult to compare their relative success rates. A veteran Senate aide noted how hard it is to get good data on this issue; even lawmakers office must rely on CRS to search for these results. Same source
Ari Fleisher had this interesting Tweet to share on his own research: link
And for your question about being a rubber stamp, well no. Back to the Slate Article:
During the 19th century, the Senate rejected 35 percent of Supreme Court nominations. Scholars cite a number of turning points leading to today's irritable process....The fact that Congress and the White House are now often of different parties has driven the Senate to play a larger role in shaping the executive branch. And the rejection of Reagan Supreme Court nominee Robert Bork in 1987, after a fierce campaign by interest groups opposing his nomination, led to the modern media era of bruising nominations. In the last years of the Clinton administration, the "consent" part of the Senate confirmation process almost completely broke down--judicial and diplomatic appointees could barely get the Senate committees to schedule hearings on their nominations
Although that's less true of Administrative slots.